Improve ASGI server documentation (#1791)

Discussions in #1757 indicate that we should document this more clearly.

docs/quickstart.rst

@@ -192,15 +192,21 @@ You can run your application using an ASGI server such as `uvicorn`. If you defi
 
 .. code-block:: bash
 
+    # assuming your application is defined as ``app`` in ``run.py``
     $ uvicorn run:app
 
-Or with gunicorn:
+Or with gunicorn (which is recommended in production).
 
 .. code-block:: bash
 
+    # assuming your application is defined as ``app`` in ``run.py``
     $ gunicorn -k uvicorn.workers.UvicornWorker run:app
 
-See the `uvicorn documentation`_ for more details.
+See the `uvicorn documentation`_ for more details or check this
+`overview of available ASGI servers`_ for other options.
+
+.. _overview of available ASGI servers: https://asgi.readthedocs.io/en/latest/implementations.html#servers.
+
 
 If you installed connexion using :code:`connexion[uvicorn]`, you can run it using the
 :code:`run` method. This is only recommended for development:

docs/v3.rst

@@ -114,6 +114,19 @@ should work, connexion comes with ``uvicorn`` as an extra:
 
     pip install connexion[uvicorn]
 
+Check :ref:`quickstart:Running your application` for more details on how to run your application
+using an ASGI server.
+
+.. warning::
+
+    You can wrap Connexion with the `ASGIMiddleware`_ offered by `a2wsgi`_ to run it with a WSGI
+    server. You will however lose the benefits offered by ASGI, and performance might be
+    impacted. You should only use this as a temporary workaround until you can switch to an ASGI
+    server.
+
+.. _ASGIMiddleware: https://github.com/abersheeran/a2wsgi#convert-asgi-app-to-wsgi-app
+.. _a2wsgi: https://github.com/abersheeran/a2wsgi
+
 Smaller breaking changes
 ------------------------