To create your Classic Patty Melt, follow these straightforward steps:

1. Prep the Onions: In a skillet over medium heat, melt 1 tablespoon of butter. Add the sliced onions, sprinkle a little salt, and sauté until golden and caramelized, about 10 minutes. Remove and set aside.

2. Form the Patties: In a bowl, combine ground beef, finely chopped onion, salt, and pepper. Mix gently and divide into two equal portions. Shape them into patties slightly larger than the slices of bread, as they will shrink while cooking.

3. Cook the Patties: In the same skillet, add the remaining tablespoon of butter. Once melted, place the beef patties in the skillet. Cook on medium-high heat for about 4-5 minutes on each side or until they reach your desired doneness.

4. Assemble the Sandwiches: Once the patties are almost done, place a slice of Swiss cheese on top of each patty, allowing it to melt. Meanwhile, start assembling the sandwich. On one slice of rye bread, layer the melted patty with caramelized onions, then top with another slice of rye bread.

5. Grill the Sandwiches: Wipe down the skillet and return to medium heat. Place the assembled sandwiches in the skillet and grill until the bread is golden brown, about 2-3 minutes per side. Ensure the cheese is thoroughly melted.