First, start the caramelized onions. Heat butter and olive oil in a skillet over low-medium heat. Add sliced onions and salt. Cook slowly, stirring occasionally for about 20 minutes until onions are soft, golden and beginning to caramelize. Set aside.
Next, prepare the patties. Divide the ground beef into 4 equal balls (about 4 ounces each). I do not recommend making them larger than this.
Prepare the buns by buttering the cut sides of each bun. Toast in a skillet or griddle over medium heat until golden. Set aside.
Cook the patties. In the same skillet or griddle, add oil and heat over medium-high heat. When the oil sizzles when water hits it, place each ball of meat on the hot surface. IMMEDIATELY smash each ball flat with a burger press or sturdy metal spatula until the patty is about 1/4-inch thick. Apply firm pressure to build a flavorful crust and hold for about 10 seconds. A sheet of parchment can be placed between the beef and the press if desired to keep it from sticking.
Season patties with salt and black pepper. Cook without moving for about 2 minutes, or until a deep brown crust forms.
Flip the patties and top each with a slice of cheese. Cook for another 1-2 minutes, or until cheese begins to melt. Use a spatula to loosen patties from the grill and set aside.
Assemble the burger. Add sauce if desired, then one cheese-topped patty on the bottom bun. Add a generous layer of caramelized onions, then the second patty. Add more caramelized onions and toppings of choice. I like dill pickles and tomato slices.
Top with the top bun, serve warm.
Notes
When I make this recipe, I make a double for my husband, and two singles for myself and my son.If you're working with a small surface area, you can cook the patties in batches.Special Burger Sauce: