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I'm a cheese person at heart, so it should go without saying that I love a good cheeseburger. I am not, however, a purist. While I can appreciate the joys of a standard burger with a slap of American cheese on top, I'm always looking for ways to improve on a good thing.
This may be sacrilege to some, but I like to mix other ingredients into my ground meat to play with the burger's flavor and texture. It was only a matter of time, then, before I added shredded cheese in an attempt to concoct the ultimate melty, meaty experience. My first experiment was so promising that I kept testing it until I perfected the idea.
One thing I learned through several iterations of this recipe: a moderate hand plays well with this method. Otherwise, you risk changing your burger's texture too much—a huge heap of cheese will make your burger fall apart in the pan. There's no way around it.
First, a note on cheese decency: I know Serious Eats champions standard American cheese on a burger, and you can debate all you want in the comments if you'd like—but it's my firm believe that a cheeseburger is only as good as the cheese you use to make it. You can have the best beef known to mankind, you can have the freshest bun crisped perfectly on the grill, and you can even have thick slices of farm-fresh organic tomatoes pulled that very morning crowning the whole ordeal. But, in my book, if you deface all that goodness with a slice of Velveeta (or similarly soulless "processed cheese food"), the whole thing collapses into a puddle of disappointing dairy dregs.
My favorite cheese for this recipe is Cowgirl Creamery's Wagon Wheel, a luscious table cheese that is semi-firm in texture, notably salty without being overly so, and carries with it a sweet-nutty flavor that seduces a burger like no other cheese I've tried. That said, you can easily incorporate any superlative cheddar or similarly semi-firm cheese into this recipe and produce impressive results. You might also try Vella Dry Jack, Kerrygold Mild White Cheddar, or a particularly lovely manchego.
Soft cheeses don't work so well here; they thin out too much when they melt and can cause your burger to turn into the world's creamiest sloppy Joe. (Or hey, go ahead and mix your meat with Époisses before frying, toss the whole thing with cooked pasta, and create a gourmet Hamburger Helper of the gods!)
While you're more than welcome to use pre-ground beef and pork in this recipe, I think you'll be pleasantly surprised by the experience of grinding your own meat for burgers. Not only are you limiting your experience to the meat of one or two animals—potentially safer when you consider how many may be involved in a single pound of pre-ground beef—but you'll notice a huge improvement in the flavor and texture of your burger. And you can choose which cut you want depending on your mood, or, like we've done here, you can mix and match different kinds of meat.
Kenji did a great post on comparing different methods for grinding burger meat, and down in the middle is some advice for using a food processor. His top tip? Make sure your meat is very chilled before grinding, to prevent it from smearing all over the place. Another tip: If you're grinding more than one cut or kind of meat, grind them in separate batches to accommodate the specific texture of each cut.