I am trying to write my own protocol handler for a JavaFX application that uses webview to access a single website. What I have done so far
My custom URLStreamHandle
By activating Logging and Tracing in the Java Control-Panel your Java-Console will print all attempts and executed network calls including those from the WebView.
You can see all HTTP & HTTPS calls and their return-code + cookie data. You might also see other protocol connections, but probably not any data sent over them.
This applies to Applets in a Browser. If you need this in a different context maybe there is a way to activate the same options by passing command line parameters.