Follow these straightforward steps to create your Cast-Iron Patty Melts:

1. Prepare the Ingredients: Begin by slicing your onion and gathering all necessary ingredients.
2. Form the Patties: In a bowl, season the ground beef with salt and pepper. Form into two equally sized patties.
3. Heat the Skillet: Place a cast-iron skillet over medium-high heat. Add 1 tablespoon of butter to the skillet.
4. Cook the Onions: Once the butter has melted, add the sliced onions to the skillet. Stir occasionally until they caramelize, about 5-7 minutes. Remove and set aside.
5. Cook the Patties: In the same skillet, add the patties. Cook for about 4 minutes on one side before flipping.
6. Add Cheese and Onions: After flipping, place a slice of cheese on each patty and add the caramelized onions on top. Cook for an additional 4-5 minutes or until the cheese is melted and the patties reach your desired doneness.
7. Toast the Bread: While the patties are finishing cooking, spread butter on one side of each slice of bread. Place the slices butter side down on another skillet over medium heat.
8. Assemble the Sandwiches: Once the bread is golden brown, carefully place one patty on each slice. Top with the second slice of bread.
9. Grill the Toasted Sandwiches: Cook both sides of the assembled sandwiches in the skillet for a few minutes, pressing down slightly with a spatula until they are nicely browned and the cheese is melted.
10. Slice and Serve: Once golden and toasty, remove from the skillet and let it cool slightly before slicing in half for serving.