How to get Kestrel serve HTTP over arbitrary Stream(s)?

Question

I have a ASP.NET web app that I need to reply over a custom transport. E.g. on the server I have an event

// the string is a description of the connection source
event Action<string, Stream> OnClientConnected; 

and I need my WebApplication to serve any HTTP requests coming from that stream and write replies to that same stream instead of the usual TCP/UDP listeners on some port.

How do I do that?