Instructions:
Caramelize the onions:
In a skillet over medium heat, melt 1 tablespoon of butter.
Add the sliced onions and cook slowly for 10–15 minutes, stirring occasionally, until they’re golden and caramelized. Remove from the skillet and set aside.
Shape and cook the patties:
Divide the ground beef into two equal portions and shape them into oval-shaped patties (to match the shape of the bread). Season both sides with salt and pepper.
In the same skillet, cook the patties over medium-high heat for about 3–4 minutes per side, until fully cooked with a nice sear. Set aside.
Assemble the sandwiches:
Butter one side of each slice of rye bread.
On the unbuttered side, layer: 1 slice of cheese, a cooked beef patty, half of the caramelized onions, another slice of cheese, and top with a second slice of bread (buttered side facing out).
Grill the sandwiches:
Heat a clean skillet or griddle over medium heat.
Cook each sandwich for 3–4 minutes per side, pressing gently with a spatula, until the bread is golden and crisp and the cheese is fully melted.
Serve:
Slice in half and serve hot with pickles, fries, or coleslaw.