In a large skillet over medium-low heat, melt 2 tablespoons of butter. Add the sliced onions and a pinch of salt. Cook slowly for 20-25 minutes, stirring occasionally, until deeply golden brown and jammy. Remove from the skillet and set aside.

While the onions cook, gently combine the ground beef, Worcestershire sauce, salt, and pepper in a mixing bowl. Do not overmix. Form the mixture into two thin, rectangular patties slightly larger than your bread slices.

Increase the skillet heat to medium-high. Cook the patties for 2-3 minutes per side until a brown crust forms and they are cooked through. Remove from the skillet and set aside.

Wipe the skillet clean. Butter one side of each slice of rye bread. Place one slice butter-side down in the skillet over medium heat. Layer with one slice of Swiss cheese, a beef patty, half of the caramelized onions, a second slice of Swiss cheese, and the final slice of bread, butter-side up.

Grill for 3-4 minutes on each side, until the bread is golden brown and crispy and the cheese is fully melted. Slice in half diagonally and serve immediately.