Making patty melts is straightforward, and following these steps will ensure a delicious outcome:

1. Caramelize the Onions: In a skillet over medium heat, melt 1 tablespoon of butter. Add the sliced onions and cook, stirring occasionally, until they are golden brown and caramelized, about 10-15 minutes. Set aside.

2. Prepare the Beef Patties: In a bowl, season the ground beef with salt and black pepper. Form the beef into two equal-sized patties, pressing lightly to flatten them.

3. Cook the Patties: In the same skillet, add a little oil if needed. Cook the patties for about 4-5 minutes on each side for medium doneness. Top each patty with a slice of cheese during the last minute of cooking to allow it to melt.

4. Grill the Bread: While the patties are cooking, heat a separate skillet or griddle over medium heat. Spread butter on one side of each slice of rye bread. Place the slices butter-side down on the hot skillet.

5. Assemble the Sandwiches: On the unbuttered side of two slices, place a cooked beef patty with melted cheese and a generous helping of caramelized onions. Top with the remaining slices of bread, unbuttered side facing the filling.

6. Grill the Sandwiches: Cook each sandwich for about 3-4 minutes on each side until golden brown and crispy. Press down slightly with a spatula to ensure everything melds beautifully together.

7. Slice and Serve: Remove the sandwiches from the skillet and let them cool for a minute. Slice in half and serve hot with additional condiments if desired.