I've made cheeseburgers by melting cheese on the finished burgers but have found that to be really messy with cheese all over the grill and plate instead of in my belly.
So here's how I now make cheeseburgers:
...and then I form the burger patty around the cheese, encapsulating it into the middle of the burger.
Cheeseburgers, ready for the grill!
And since this is Oregon, the grill is parked in a semi-dry spot under a tree because I don't like to stand in the rain to grill my cheeseburgers.
I'm not much of a food photographer, as you can tell, or I would show you the oozy, melted cheese in the middle of the burger that hasn't slid off onto the grill or on the plate.
Bring on summer.