Prepare the onions: Finely slice the onion and set it aside for cooking later.
Shape the beef: Divide the ground beef into four equal portions, rolling each into a ball. Flatten them into roughly 3-inch-wide patties. Generously season both sides with salt, black pepper, and garlic powder.
Cook the patties: Heat 2 tablespoons of butter in a skillet over medium-high heat. Place the patties in the pan and immediately layer sliced onions on top of each one. Tear off a small piece of parchment paper, press it over a burger, then use a spatula to firmly smash it down, ensuring the edges crisp up nicely. Remove the parchment paper and repeat with the remaining patties. Sprinkle the onions with a little salt and pepper for added flavor.
Flip and finish cooking: Allow the burgers to cook undisturbed until the bottoms develop a deep brown crust, about 2–3 minutes. Carefully flip each patty. If the onions haven’t stuck to the meat, gently press them underneath with the spatula. Cook for another 1–2 minutes, ensuring they’re well-browned and fully cooked.
Add Worcestershire sauce: Lightly drizzle Worcestershire sauce over the patties and let them cook for an additional 45–60 seconds. Once done, transfer them to a plate and remove the skillet from heat.
Assemble the sandwiches: Spread a thin layer of softened butter on one side of each bread slice. Lay four slices, butter-side down, on a cutting board or plate. Top each with a slice of American cheese, then place a cooked patty on top. Add another cheese slice and cover with a second piece of bread, buttered-side facing up.
Toast the sandwiches: Return the skillet to medium heat. Arrange the sandwiches in the pan and cook until the bottoms turn a deep golden brown, about 1–2 minutes. Flip them carefully and continue cooking until the cheese is fully melted and the bread is crisp and golden on the other side, another 1–2 minutes.
Serve immediately: Enjoy these hot, crispy sandwiches fresh off the skillet with your favorite side dishes or condiments.