In a large skillet, melt 2 tbsp of butter over medium-low heat. Add the sliced onions and cook slowly, stirring occasionally, for 25-30 minutes until they are deeply golden brown and sweet. Remove from skillet and set aside.

In another skillet, melt 1 tbsp of butter over medium-high heat. Add the mushrooms and cook until browned, about 5-7 minutes. Add the minced garlic and Worcestershire sauce, and cook for another minute until fragrant. Season with salt and pepper to taste. Set aside.

Divide the ground chuck into two equal portions and form into thin oval patties slightly larger than your bread slices. Season both sides with salt and pepper. Cook in the skillet over medium-high heat for 3-4 minutes per side. In the last minute of cooking, top each patty with the sautéed mushrooms and one slice of Swiss cheese.

Spread softened butter on one side of each slice of sourdough bread. On the unbuttered side of two slices, place one slice of Swiss cheese, a cooked patty, and a generous portion of caramelized onions.

Top with the remaining slices of bread, butter-side-out. Grill the sandwiches in the skillet over medium heat for 3-4 minutes per side, until the bread is golden and crispy, and the cheese is fully melted.

Slice the melts in half diagonally and serve immediately.