Place the ground beef in a large mixing bowl. Using a small grater, grate the frozen butter into the ground beef. Add in salt and pepper to your taste. Mix it thoroughly by hand and divide the mixture into four portions. Form each portion into a patty and set aside.
1 pound ground beef, 4 tablespoons unsalted butter, frozen, Salt and pepper, to taste
Preheat a large cast iron pan or flat griddle over medium-high heat. Add 1 tablespoon of butter to the pan and allow it to heat.
2 tablespoons butter, divided
Add the onions to the pan and cook, stirring frequently, for 3 to 5 minutes. Move the onions to one side of the pan.
1 medium sweet onion, sliced
Add the remaining tablespoon of butter, and add the burger patties to the skillet next to the onions. Cook the burgers to desired doneness, checking the internal temperature with an instant read thermometer for your desired temperature.
Once the burger is flipped, add a slice of American cheese to each patty. Divide the sautéed onions among the burgers and top with a second slice of American cheese.
8 slices American cheese
Cover the skillet to let the burgers to finish cooking and to melt the cheese.
While the cheese melts, lightly baste the cut side of the bun with the pan drippings. Place the bun cut side down in the skillet to lightly toast them.
4 Brioche buns
Remove the buns from the skillet and place the burger on the bottom bun. Top with more sautéed onions and desired toppings such as lettuce and condiments.