Ingredients:

4 burger patties (fresh or frozen)
8 slices of bread (sourdough or your choice)
8 slices of cheese (cheddar, Swiss, or a mix for extra flavor)
1 large onion, thinly sliced
2 tablespoons butter, plus more for spreading on bread
Salt and pepper, to taste
Optional: mustard, mayonnaise, or your favorite condiment

Instructions:

Cook the Patties:

Season the burger patties with salt and pepper.
Heat a skillet over medium-high heat. Cook the patties to your preferred doneness, about 3-4 minutes per side for medium. Remove and set aside.
Caramelize the Onions:

In the same skillet, reduce heat to medium. Add 2 tablespoons of butter.
Add the sliced onions, season with a pinch of salt, and cook, stirring occasionally, until they are golden brown and caramelized, about 15-20 minutes. Remove from the skillet and set aside.

Assemble the Patty Melts:

Spread butter on one side of each bread slice.
On the non-buttered side of four slices, place a slice of cheese, a cooked burger patty, a quarter of the caramelized onions, another slice of cheese, and finally top with another slice of bread, buttered side out.

Grill the Sandwiches:

Heat the skillet over medium heat.
Cook each sandwich until the bread is golden brown and the cheese has melted, about 3-4 minutes per side. Press down lightly with a spatula for an even grill.
Serve Warm:

Cut the patty melts in half and serve immediately. Enjoy with a side of pickles or your favorite chips!