Cook the patties: In the same skillet (no need to wipe it out), increase the heat to medium-high. Add the beef patties and cook 3–4 minutes per side, or until nicely browned with crispy edges and cooked to your desired doneness. Transfer the cooked patties to a plate and turn the heat down to medium-low.
Butter the bread: While the patties rest, spread the remaining 4 tablespoons of softened butter evenly on one side of each bread slice. This is what gives you that greasy, golden crunch, so make sure you go all the way to the edges.
Assemble in the pan: Place 4 slices of bread, buttered side down, into the skillet. Top each with 1 slice of cheese, a generous scoop of the caramelized onions, one beef patty, and another slice of cheese. Cap each with a second slice of bread, buttered side up.
Grill the patty melts: Cook the sandwiches over medium-low heat for 3–4 minutes per side, pressing gently with a spatula, until the bread is deep golden brown and crisp and the cheese is fully melted and gooey in the center. If the bread is browning too fast, lower the heat and give the cheese more time to melt.
