You could try submitting a treatment. If you don't know what that is, it's basically a long synopsis with notes about the characters and such, and it can run for a dozen pages or more. For a TV series, it could be the beginning of the show's 'bible'. Being 'uniquely qualified' is a good draw. The treatment should be clever in its own right, highlighting the funniest aspects of your story.

If anyone buys into the concept, they may ask for your scripts as a writing sample. If they really love the thing, there's any number of things they might do. Making you the show runner (i.e. 'creator') and hiring a bunch of their own writers is probably the least likely scenario. But it could happen. They could also have you jump through hoops with notes and rewrites and changes and then drop the thing altogether with no warning. It's a tough business. You got to try, though.