A good place to get started would be to look at the Twitch’s sample extensions. Hello World has a backend for Node.js and shows how the extension can send HTTP requests to the EBS which is a web accessible server listening for HTTP requests, verifies the JWT, and handles the requests appropriately (and in the case of this sample extension the EBS uses extension pubsub to broadcast a message to all extension users on that channel but it could just as easily respond to just the user who sent the request).
As well as HTTP, another option if you need real-time 2 way communication would be to use web sockets. Which is best for your use case depends on your extension needs, the main requirement of either method of communication with the EBS is that you do it securely over HTTPS or WSS.