Embedded WSGI backend for Python desktop app using webkit
Earlier today I saw exactly what you're asking for -- a way to call WSGI through an API without actually connecting over the network. However, it shouldn't be that hard. 
On a side note, you might want to look at PySide, of particular interest to you may be the ability to bind python elements to DOM events, so if you're just looking to trigger python code that's an even shorter route. 
If you give some more detail on what you're hoping to achieve we might be able to dial it in for you.
Disclaimer: I'm not very familiar with any of the things mentioned in the question title.
Would it be possible to use a browser control (like Webkit) as a frontend for a WSGI app (using a framework like Flask) without starting a local WSGI server?
Basically the requests and responses are managed by a middle layer between the HTML UI and the WSGI backend. A certain URI could mean "Local", for instance "local://" or something similar, and will be routed to the embedded WSGI app with all the original headers etc.
You will lose any features that a normal WSGI server provides unless you implement it yourself or somehow embed a server that is also usable via an API instead of real HTTP requests.
Now that I think of it, this is the only real requirement: A WSGI server that is callable via an API and not just real HTTP requests.
I know the usefulness of this is questionable (and maybe doesn't even make sense). My question is whether this is at all possible?
EDIT: Here's another way of putting it:
I want a single codebase to be both a web app and a desktop app, using an HTML frontend and a Python backend. I don't want to run a server on any port for the desktop app. What's the easiest way to achieve this?