Prepare the Sauce:

In a small bowl, mix together mayonnaise, ketchup, horseradish sauce, paprika, and garlic powder until well combined. Set aside.

Caramelize the Onions:

In a skillet, heat butter and oil over medium heat. Add the sliced onions and a pinch of salt. Cook, stirring occasionally, until the onions are caramelized and deeply golden, about 15-20 minutes. Remove from the skillet and set aside.

Form and Cook the Patties:

Divide the ground beef into two equal portions and form into thin patties slightly larger than your bread slices. Season both sides with salt and pepper.

Heat the same skillet over medium-high heat. Add the patties and cook for about 3-4 minutes on each side or until well-browned and cooked to your preference.

Assemble the Patty Melts:

Butter one side of each slice of bread. Spread a generous amount of the prepared sauce on the non-buttered side.

On two slices, place a slice of American cheese, a cooked beef patty, half of the caramelized onions, a slice of Monterey Jack cheese, and top with another slice of bread, buttered side out.

Grill the Patty Melts:

Heat a clean skillet or griddle over medium heat.

Place the assembled sandwiches in the skillet. Grill for about 3-4 minutes on each side, pressing down slightly with a spatula, until the bread is toasted golden brown and the cheese is melted.