In 1924, according to his obit in TIME magazine, 16 year old Lionel Clark Sternberger, "experimentally dropped a slab of American cheese on a sizzling hamburger while helping out at his father's sandwich shop in Pasadena, thereby inventing the cheeseburger."
Thank you Mr. Sternberger for a great taste combo and an American icon.
A cheeseburger can be crafted from practically any other hamburger style with the simple addition of cheese, and many cheeses will do. There are only two important guidelines:
1) The cheese must be melted. It cannot be cold or hard.
2) The chosen cheese must enhance the composition of the sandwich, not clash with it. There are two ways to go with adding dairy to your cow: Melting cheese, or spreading cheese.
Let's discuss the melting method first.
How to add the cheese
Whatever cooking method you use, the cheese is the last thing to go on. Most of the cheeses below melt quickly, within 2 minutes. So you should only apply it after one side is finished cooking, when you are within 2 minutes of finishing the other side.
If you are grilling your burger, lay the cheese on top, and then close the lid so the cheese will melt. Depending on the cheese, 2 to 3 minutes should do it. Be careful not to overcook the meat while melting the cheese. You might even want to move the patty off direct heat while you melt the cheese. Another trick is to cap the burger like they do in some diners. Just add the cheese, put a metal mixing bowl over the burger, and it should melt in as little as 30 seconds. A coffee can or baking pan will work fine.
In a frying pan, put the lid on, but not tight. Leave a good sized crack so steam can escape. If you don't have a lid, cover the pan with a metal baking pan or cookie sheet.
On a griddle, use a metal bowl or pan to trap the heat and melt the cheese.
Under a broiler, pull the burgers out, lay on the cheese, and slide it back under the broiler, about 2" below the heat source. Leave the door open and stand there and watch, because it can melt quickly. As soon as it starts to bubble, you're done.
Here's another trick. If you are using caramelized onions, sautéd mushrooms, or even raw onion, put them on before the cheese. As the cheese melts it will help anchor the toppings in place so they don't fall off as easily.
Cheeses for melting
The issues surrounding the selection of a cheese are: Taste, meltability, color, and cooking method.
The prototypical American cheeseburger has a slice of bright yellow American cheese or cheddar. My fave is sharp cheddar for flavor and tradition. Better still, a smoked cheddar.
But there's no reason why you can't use another melting cheese. Smoked gouda, Muenster, jack, pepper jack, brie, provalone, cambozola, Swiss,and havarti are good choices. Just don't mask the meat with too much. Slice it 1/8" thick (or grate it and pile it on 1/4" thick because there's a lot of air in grated cheese). Add more if you wish, but remember, the thicker the cheese, the longer it takes to melt, so factor that into your cooking time.
Gruyere is nice but it doesn't melt well, so grate it first. Crumbled blue cheese is popular, although it doesn't melt well either. It is especially good if you can put it under a flame to broil and brown it a bit, and I like it best on top of thin apple slices and caramelized onions.
Cheeses for spreading
Another approach is to use a spreadable cheese that doesn't need to be melted. It can go on the underside of the bun top, or right on the patty in a blob so it can spread with heat and pressure from the bun.
Pimento cheese spread is very popular in the South, particularly South Carolina and Georgia. My faves are my home-made boursin (laced with garlic), or herbed fresh chevre (herbaceous and tangy). The Cherry Cricket in Denver is famous for their Cricket Burger with a slab of cream cheese and some minced jalapeño on top.
Other options include cheddar spread with port wine, blue cheese spread, beer cheese, or amp it up by mixing cream cheese with chili sauce or horseradish. Or try the chevre with a balsamic reduction instead of ketchup.
Toppings and bottomings
For more ideas
Hard core cheeseburger lovers will get a few more laughs and learn a thing or two from Kevin Pang's The Cheeseburger Show.
The Cheese & Burger Society is a fun site sponsored by Wisconsin Cheese and it has some creative combos and beautiful pictures.
A note about safety and proper cooking of burgers
Undercooked ground meat and sausage can kill. It can happen to you or a loved one. It is primarily a problem in ground meats, not steaks. I urge you to click this link to read more about dangerous pathogens in burgers and other ground meats and how to prevent food-borne illness. If you see pink ground meat on this website, it is meat I have pasteurized as described in the above link.