expeditious

It's slowly looking like my webapp should probably instead be a desktop app that talks in the background to a central server. I say this because it needs features like a webapp (log in as admin to the site, talk to db on webserver, see changes happen as they're made by others who are logged in, etc.), but it's complex enough that it feels like I should use GTK/Qt/whatever and run it on the desktop instead of using some in-browser overgrown JS GUI framework. Also, I am just not a fan of complex web pages that try to act like applications.

How can I have a desktop GUI app talk to the webserver securely? Should I just have my app send GET/POST requests over SSL? Have it use cookies for session management the way my webapp would?