Melt 2 tablespoons unsalted butter in a cast iron skillet over medium-low heat and add the thinly sliced onions. Cook 25-30 minutes, stirring as needed, until deeply golden.

Divide the 80/20 ground beef into 4 balls, then season each with Worcestershire sauce, garlic powder, salt, and pepper. Press the seasoning evenly over the surface.

Heat the cast iron skillet over high heat, then smash each beef ball thin and flat in the pan. Cook 2-3 minutes per side until browned and crisp at the edges.

Add the remaining butter to the skillet and toast the rye bread slices until golden. Cook briefly until the bread feels crisp.

Whisk together mayo, ketchup, Dijon, and the remaining Worcestershire sauce to make the special sauce. Spread a layer on the toasted rye bread.

Assemble each melt by layering toasted rye bread, special sauce, caramelized onions, a smash patty, Swiss cheese, sharp American or cheddar cheese, extra onions, and the second slice of toast. Keep the cheese centered over the patty.

Return the assembled sandwiches to the cast iron skillet and press lightly. Cook 1-2 minutes per side until the cheese is fully melted.