Preheat the skillet over medium heat.
Season the ground beef with garlic powder, salt, and pepper, then form it into four equally sized patties.
Cook the burger patties on the skillet for about 4-5 minutes on each side, or until they reach your desired doneness.
While the burgers are cooking, assemble the grilled cheese sandwiches by placing cheese slices between two pieces of bread.
Once burgers are done, transfer them to a plate to rest briefly. In the same skillet, melt 1 tablespoon of butter and add the assembled sandwiches.
Grill the sandwiches for about 3-4 minutes per side, pressing down gently until golden and crispy, and the cheese is melted.
Remove the sandwiches, slice them in half, and immediately place a burger patty in between each pair of grilled cheese slices.
Serve your grilled cheese burgers immediately, accompanied by your favorite condiments or sides.