Step 1

Heat 2 tablespoons of butter in a medium skillet over medium heat. Add the onions and sprinkle with the thyme, 1/2 teaspoon salt, and several grinds of pepper. Cook, occasionally stirring, until the onions are browned and tender, about 20 minutes. Turn off the heat and transfer the onions to a bowl adding the teaspoon of Worcestershire sauce, and set aside.

Step 2

Evenly spread mayonnaise over one side of each slice of bread. Top a slice with the onion mixture and then sandwich the onions with a slice of sharp cheddar and a slice of swiss cheese.-side in. Season with salt and pepper. Add a Tablespoon of butter to the skillet and griddle the sandwich over medium heat until golden brown on the first side, about 5 minutes. Flip and cook until the cheese is melted and the exteriors are crispy, about 5 minutes more.