diff --git a/pandas/_typing.py b/pandas/_typing.py
index 7f01bcaa1c50e..a4501199fd3a3 100644
--- a/pandas/_typing.py
+++ b/pandas/_typing.py
@@ -30,6 +30,7 @@
     from typing import final
 
     from pandas._libs import Period, Timedelta, Timestamp
+    from pandas._libs.missing import NAType
 
     from pandas.core.dtypes.dtypes import ExtensionDtype
 
@@ -44,9 +45,11 @@
     from pandas.core.window.rolling import BaseWindow
 
     from pandas.io.formats.format import EngFormatter
+
 else:
     # typing.final does not exist until py38
     final = lambda x: x
+    NAType = Any
 
 
 # array-like
diff --git a/pandas/core/arrays/_mixins.py b/pandas/core/arrays/_mixins.py
index 07862e0b9bb48..ae5b6b164fb8d 100644
--- a/pandas/core/arrays/_mixins.py
+++ b/pandas/core/arrays/_mixins.py
@@ -1,6 +1,6 @@
 from __future__ import annotations
 
-from typing import Any, Optional, Sequence, Type, TypeVar, Union
+from typing import Any, Optional, Sequence, Type, TypeVar, Union, overload
 
 import numpy as np
 
@@ -25,6 +25,7 @@
 NDArrayBackedExtensionArrayT = TypeVar(
     "NDArrayBackedExtensionArrayT", bound="NDArrayBackedExtensionArray"
 )
+EAScalarOrMissing = object  # both scalar value and na_value can be any type
 
 
 class NDArrayBackedExtensionArray(ExtensionArray):
@@ -214,9 +215,21 @@ def __setitem__(self, key, value):
     def _validate_setitem_value(self, value):
         return value
 
+    @overload
+    # error: Overloaded function signatures 1 and 2 overlap with incompatible
+    # return types  [misc]
+    def __getitem__(self, key: int) -> EAScalarOrMissing:  # type: ignore[misc]
+        ...
+
+    @overload
+    def __getitem__(
+        self: NDArrayBackedExtensionArrayT, key: Union[slice, np.ndarray]
+    ) -> NDArrayBackedExtensionArrayT:
+        ...
+
     def __getitem__(
         self: NDArrayBackedExtensionArrayT, key: Union[int, slice, np.ndarray]
-    ) -> Union[NDArrayBackedExtensionArrayT, Any]:
+    ) -> Union[NDArrayBackedExtensionArrayT, EAScalarOrMissing]:
         if lib.is_integer(key):
             # fast-path
             result = self._ndarray[key]
diff --git a/pandas/core/arrays/base.py b/pandas/core/arrays/base.py
index a0a51495791d1..8cfafd8b52da8 100644
--- a/pandas/core/arrays/base.py
+++ b/pandas/core/arrays/base.py
@@ -20,6 +20,7 @@
     TypeVar,
     Union,
     cast,
+    overload,
 )
 
 import numpy as np
@@ -51,6 +52,7 @@
 _extension_array_shared_docs: Dict[str, str] = dict()
 
 ExtensionArrayT = TypeVar("ExtensionArrayT", bound="ExtensionArray")
+EAScalarOrMissing = object  # both scalar value and na_value can be any type
 
 
 class ExtensionArray:
@@ -256,9 +258,19 @@ def _from_factorized(cls, values, original):
     # Must be a Sequence
     # ------------------------------------------------------------------------
 
+    @overload
+    # error: Overloaded function signatures 1 and 2 overlap with incompatible
+    # return types  [misc]
+    def __getitem__(self, item: int) -> EAScalarOrMissing:  # type: ignore[misc]
+        ...
+
+    @overload
+    def __getitem__(self, item: Union[slice, np.ndarray]) -> ExtensionArray:
+        ...
+
     def __getitem__(
         self, item: Union[int, slice, np.ndarray]
-    ) -> Union[ExtensionArray, Any]:
+    ) -> Union[ExtensionArray, EAScalarOrMissing]:
         """
         Select a subset of self.
 
diff --git a/pandas/core/arrays/datetimelike.py b/pandas/core/arrays/datetimelike.py
index 30674212239bf..06cf8450f9a21 100644
--- a/pandas/core/arrays/datetimelike.py
+++ b/pandas/core/arrays/datetimelike.py
@@ -13,6 +13,7 @@
     TypeVar,
     Union,
     cast,
+    overload,
 )
 import warnings
 
@@ -266,9 +267,19 @@ def __array__(self, dtype=None) -> np.ndarray:
             return np.array(list(self), dtype=object)
         return self._ndarray
 
+    @overload
+    def __getitem__(self, key: int) -> DTScalarOrNaT:
+        ...
+
+    @overload
+    def __getitem__(
+        self: DatetimeLikeArrayT, key: Union[slice, np.ndarray]
+    ) -> DatetimeLikeArrayT:
+        ...
+
     def __getitem__(
-        self, key: Union[int, slice, np.ndarray]
-    ) -> Union[DatetimeLikeArrayMixin, DTScalarOrNaT]:
+        self: DatetimeLikeArrayT, key: Union[int, slice, np.ndarray]
+    ) -> Union[DatetimeLikeArrayT, DTScalarOrNaT]:
         """
         This getitem defers to the underlying array, which by-definition can
         only handle list-likes, slices, and integer scalars
diff --git a/pandas/core/arrays/datetimes.py b/pandas/core/arrays/datetimes.py
index 057162fedaa98..a05dc717f83c1 100644
--- a/pandas/core/arrays/datetimes.py
+++ b/pandas/core/arrays/datetimes.py
@@ -1,5 +1,5 @@
 from datetime import datetime, time, timedelta, tzinfo
-from typing import Optional, Union, cast
+from typing import Optional, Union
 import warnings
 
 import numpy as np
@@ -444,11 +444,9 @@ def _generate_range(
             )
 
         if not left_closed and len(index) and index[0] == start:
-            # TODO: overload DatetimeLikeArrayMixin.__getitem__
-            index = cast(DatetimeArray, index[1:])
+            index = index[1:]
         if not right_closed and len(index) and index[-1] == end:
-            # TODO: overload DatetimeLikeArrayMixin.__getitem__
-            index = cast(DatetimeArray, index[:-1])
+            index = index[:-1]
 
         dtype = tz_to_dtype(tz)
         return cls._simple_new(index.asi8, freq=freq, dtype=dtype)
diff --git a/pandas/core/arrays/masked.py b/pandas/core/arrays/masked.py
index caed932cd7857..ca4cd0b63722b 100644
--- a/pandas/core/arrays/masked.py
+++ b/pandas/core/arrays/masked.py
@@ -1,11 +1,20 @@
 from __future__ import annotations
 
-from typing import TYPE_CHECKING, Any, Optional, Sequence, Tuple, Type, TypeVar, Union
+from typing import (
+    TYPE_CHECKING,
+    Optional,
+    Sequence,
+    Tuple,
+    Type,
+    TypeVar,
+    Union,
+    overload,
+)
 
 import numpy as np
 
 from pandas._libs import lib, missing as libmissing
-from pandas._typing import Scalar
+from pandas._typing import NAType, Scalar
 from pandas.errors import AbstractMethodError
 from pandas.util._decorators import cache_readonly, doc
 
@@ -30,6 +39,8 @@
 
 
 BaseMaskedArrayT = TypeVar("BaseMaskedArrayT", bound="BaseMaskedArray")
+# scalar value is a Python scalar, missing value is pd.NA
+ScalarOrNAType = Union[Scalar, NAType]
 
 
 class BaseMaskedDtype(ExtensionDtype):
@@ -102,9 +113,19 @@ def __init__(self, values: np.ndarray, mask: np.ndarray, copy: bool = False):
     def dtype(self) -> BaseMaskedDtype:
         raise AbstractMethodError(self)
 
+    @overload
+    # error: Overloaded function signatures 1 and 2 overlap with incompatible return
+    # types  [misc]
+    def __getitem__(self, item: int) -> ScalarOrNAType:  # type: ignore[misc]
+        ...
+
+    @overload
+    def __getitem__(self, item: Union[slice, np.ndarray]) -> BaseMaskedArray:
+        ...
+
     def __getitem__(
         self, item: Union[int, slice, np.ndarray]
-    ) -> Union[BaseMaskedArray, Any]:
+    ) -> Union[BaseMaskedArray, ScalarOrNAType]:
         if is_integer(item):
             if self._mask[item]:
                 return self.dtype.na_value
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 9ea0ff323a33d..e8a2565bed9b6 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -3222,14 +3222,8 @@ def _get_nearest_indexer(self, target: "Index", limit, tolerance) -> np.ndarray:
         right_indexer = self.get_indexer(target, "backfill", limit=limit)
 
         target_values = target._values
-        # error: Unsupported left operand type for - ("ExtensionArray")
-        left_distances = np.abs(
-            self._values[left_indexer] - target_values  # type: ignore[operator]
-        )
-        # error: Unsupported left operand type for - ("ExtensionArray")
-        right_distances = np.abs(
-            self._values[right_indexer] - target_values  # type: ignore[operator]
-        )
+        left_distances = np.abs(self._values[left_indexer] - target_values)
+        right_distances = np.abs(self._values[right_indexer] - target_values)
 
         op = operator.lt if self.is_monotonic_increasing else operator.le
         indexer = np.where(
@@ -3248,8 +3242,7 @@ def _filter_indexer_tolerance(
         indexer: np.ndarray,
         tolerance,
     ) -> np.ndarray:
-        # error: Unsupported left operand type for - ("ExtensionArray")
-        distance = abs(self._values[indexer] - target)  # type: ignore[operator]
+        distance = abs(self._values[indexer] - target)
         indexer = np.where(distance <= tolerance, indexer, -1)
         return indexer
 
@@ -4546,9 +4539,8 @@ def asof_locs(self, where: "Index", mask) -> np.ndarray:
 
         result = np.arange(len(self))[mask].take(locs)
 
-        # TODO: overload return type of ExtensionArray.__getitem__
-        first_value = cast(Any, self._values[mask.argmax()])
-        result[(locs == 0) & (where._values < first_value)] = -1
+        first = mask.argmax()
+        result[(locs == 0) & (where._values < self._values[first])] = -1
 
         return result
 
diff --git a/pandas/core/indexes/period.py b/pandas/core/indexes/period.py
index 67dea6d1df8ed..c0a3b95499b3d 100644
--- a/pandas/core/indexes/period.py
+++ b/pandas/core/indexes/period.py
@@ -1,5 +1,5 @@
 from datetime import datetime, timedelta
-from typing import Any, cast
+from typing import Any
 
 import numpy as np
 
@@ -673,10 +673,7 @@ def difference(self, other, sort=None):
 
         if self.equals(other):
             # pass an empty PeriodArray with the appropriate dtype
-
-            # TODO: overload DatetimeLikeArrayMixin.__getitem__
-            values = cast(PeriodArray, self._data[:0])
-            return type(self)._simple_new(values, name=self.name)
+            return type(self)._simple_new(self._data[:0], name=self.name)
 
         if is_object_dtype(other):
             return self.astype(object).difference(other).astype(self.dtype)
diff --git a/pandas/core/internals/blocks.py b/pandas/core/internals/blocks.py
index 08fe67a2979da..c170ebb844c5a 100644
--- a/pandas/core/internals/blocks.py
+++ b/pandas/core/internals/blocks.py
@@ -511,6 +511,7 @@ def make_a_block(nv, ref_loc):
             return [block]
 
         # ndim > 1
+        assert isinstance(new_values, np.ndarray), type(new_values)
         new_blocks = []
         for i, ref_loc in enumerate(self.mgr_locs):
             m = mask[i]