Just say you have a quite large and complicated desktop application written in objective-c/cocoa written properly in MVC. You then wish to replace the V and C so that it is
You can leave the server almost as-is. I'd run it as a daemon in the background.
I'd split the controller part. One part of it resides on the server as a connection between HTTP requests and the daemon.
The second part of the controller is written in Javascript in the browser, exchanging data with the server and updating the GUI.
The view part is written completely in javascript.
You could - if you want - leave out the controller on the server and make the model understand HTTP requests.
For the Controller / View part consider using a framework.