Heat vegetable oil over medium heat in a skillet and add diced onions, sauteing until they start to brown. Remove from the onions from the pan and set aside. For four to six burgers, you shouldn't need more than one onion.

Preheat your oven to between 375 and 400 degrees Fahrenheit and season your ground beef with salt, pepper and any other seasonings you prefer.

Form the ground beef into equal-sized ball, and with your thumb, and press a deep hole into each ball of ground beef. The hole should be halfway deep into the ground beef ball.

Stuff shredded or diced cheese into the hole, along with some of the sauteed onions. You can use any type of cheese you prefer on your burgers. For four to six burgers, you should only need about a 1/2 cup of cheese, divided evenly among the burger patties.

Reshape the ground beef to cover the hole, fully enveloping the cheese in ground beef and flatten each patty to a 3/4-inch thickness.

Place the prepared patties on a broiler pan or a wire rack that sits on a baking tray. This allows the fat to drip away from the burgers, and avoids overly greasy burgers.

Bake in the oven for roughly 15 to 25 minutes, until the patties have an internal temperature of at least 160 F and are cooked to your liking. The time may vary, depending on the thickness of your patties. Serve them hot on burger buns.