What would be the best/lightest GUI-via-the-browser framework to employ with a program compiled as a Cosmopolitan fat binary?

(say, Qt WebAssembly? ...something else?)

Or is there a even better route to run-anywhere Cosmopolitan apps with a GUI?

Perhaps, by the same authors, redbean, which "embeds Lua, SQLite, and MbedTLS into a fork() driven application server" ... " a great fit for when you want to build an app that's vertically integrated into a single tiny file that runs on nearly all PCs and servers". It looks like as of now, greenbean exists as well.

I second this. I'm a Java dev and so have been porting Spring Petclinic to redbean using fullmoon which is a Lua framework built on top of redbean by Paul Kulchenko (who also is the author of ZeroBrane studio - a nice lightweight Lua ide which I have been using).

https://github.com/pkulchenko/fullmoon

So far it's been a lovely experience and Paul is super responsive. Redbean is massively faster at startup so I can build/bounce to do hot reload in real time basically where the spring app takes about 6 seconds to start up.