Mix meat and form patties - In a mixing bowl, combine beef, garlic powder, salt, and pepper. Mix gently until combined, careful to not over mix. Form the meat into 4 equal-sized patties and use your thumb to make an indentation in the middle of each patty. This prevents the meat from puffing up in the center when cooked.
1 lb ground beef, 2 teaspoon fine sea salt or kosher salt, 1 teaspoon garlic powder, 2 teaspoon freshly ground black pepper
Cook patties - Heat a skillet or griddle over medium heat and add oil. Once the skillet heats for about 2 minutes, add the patties to the pan. For medium rare, cook for 4 minutes on each side; for medium, cook 5 minutes on each side. If the pan is small, cook 2 patties at a time.
1 tablespoon neutral cooking oil
Add cheese - In the last minute of cooking, add cheese on top of each patty if desired and place a lid on the skillet to allow the cheese to melt. Remove the lid from the skillet and remove the skillet from the heat.
4 cheese slices
Toast buns - While the patties cook, toast the hamburger buns until just golden brown and still soft.
4 burger buns
Cook eggs - While burgers cook, heat butter in separate cast iron skillet or pan over low-medium heat. Once the butter is melted and slightly foamy, crack the egg onto skillet and sprinkle salt and pepper on top. Cook for about 2 to 2½ minutes. Once the egg whites go from clear to white and edges start to crisp, use spatula to transfer egg to burger.
4 eggs, 2 teaspoon butter
Assemble burgers - Assemble on toasted buns with ketchup or your favorite spread, lettuce, tomato, raw sliced or grilled onions, or with your preferred toppings.
4 tomato slices, lettuce, grilled or sliced raw onions, ketchup