In a small saucepan, melt butter and cook onions over low heat. Add thyme sprigs and cook onions for about an hour, stirring on occasion. Season with salt to taste. Discard thyme sprigs when done.
Meanwhile mix together mayonnaise and garlic. Season to taste with salt and pepper. Refrigerate until ready to use.
Mix together ground beef and Worcestershire sauce. Form into patties and then season with salt and pepper.
Cook patties in a skillet. Add cheese after flipping. Top with caramelized onions and top with a second piece of cheese; cook until patty is cooked through and cheese has melted.
Assemble burgers by topping bottom bun with tomato, lettuce, bacon, burger patty, and a top bun that has been smothered by garlic mayo.