lib: Use proxy to access default error target

Fixes usage of self-signed certs with JupyterHub with CHP.
Original issue here:
jupyterhub/zero-to-jupyterhub-k8s#1742 (comment)

Author: chancez

lib/configproxy.js

@@ -421,7 +421,6 @@ class ConfigurableProxy extends EventEmitter {
     // custom error server gets `/CODE?url=/escapedUrl/`, e.g.
     // /404?url=%2Fuser%2Ffoo
 
-    var proxy = this;
     var errMsg = "";
     this.statsd.increment("requests." + code, 1);
     if (e) {
@@ -439,34 +438,28 @@ class ConfigurableProxy extends EventEmitter {
     }
     this.log.error("%s %s %s %s", code, req.method, req.url, errMsg);
     if (!res) {
+      this.log.debug("Socket error, no response to send");
       // socket-level error, no response to build
       return;
     }
     if (this.errorTarget) {
-      var urlSpec = URL.parse(this.errorTarget);
-      urlSpec.search = "?" + querystring.encode({ url: req.url });
-      urlSpec.pathname = urlSpec.pathname + code.toString();
-      var secure = /https/gi.test(urlSpec.protocol) ? true : false;
-      var url = URL.format(urlSpec);
-      var errorRequest = (secure ? https : http).request(url, function(upstream) {
-        ["content-type", "content-encoding"].map(function(key) {
-          if (!upstream.headers[key]) return;
-          if (res.setHeader) res.setHeader(key, upstream.headers[key]);
-        });
-        if (res.writeHead) res.writeHead(code);
-        upstream.on("data", data => {
-          if (res.write) res.write(data);
-        });
-        upstream.on("end", () => {
-          if (res.end) res.end();
-        });
-      });
-      errorRequest.on("error", e => {
+      var target = URL.parse(this.errorTarget);
+      var secure = target.protocol.toLowerCase() === "https:";
+      target.search = "?" + querystring.encode({ url: req.url });
+      target.pathname = target.pathname + code.toString();
+
+      if (secure && this.options.clientSsl && secure) {
+        target.key = this.options.clientSsl.key;
+        target.cert = this.options.clientSsl.cert;
+        target.ca = this.options.clientSsl.ca;
+      }
+
+      this.log.debug("Requesting custom error page: %s", target.format());
+      this.proxy.web(req, res, { target: target }, (err) => {
         // custom error failed, fallback on default
-        this.log.error("Failed to get custom error page: %s", e);
+        this.log.error("Failed to get custom error page: %s", err);
         this._handleProxyErrorDefault(code, kind, req, res);
       });
-      errorRequest.end();
     } else if (this.errorPath) {
       var filename = path.join(this.errorPath, code.toString() + ".html");
       if (!fs.existsSync(filename)) {