Yes, I just ate this.  That's a Quarter Pounder with Cheese, with the bun removed and replaced with two grilled cheese sandwiches (which are on the kid's menu at McDonald's, FYI).  I believe this type of burger is known as a "Fatty Melt", though I can't find any evidence that anyone has tried this at McDonald's before.  Or maybe they just weren't foolish enough to admit to it in public.

Somehow, this was much more awesome in theory than in execution.  I mean, it was okay (albeit absurdly fattening) but the cheese sort of overwhelmed everything else.  Plus: I ate this about an hour ago and I'm still feeling pretty queasy.  I'd probably advise against trying this (though it might work a bit better with an Angus Burger, since the patty there is a bit thicker and more flavourful, so it would probably stand up to the grilled cheese a bit better.  Hmmm....).