Caramelize onions in 2 tbsp butter over medium heat, about 15–20 minutes.
Season beef with salt and pepper; shape into 4 flat patties.
In a bowl, mix mayo, ketchup, relish, Worcestershire, garlic, and onion powders.
Sear patties 3–4 minutes per side in skillet with 1 tbsp butter. Set aside.
Spread secret sauce on 4 bread slices, layer cheese, patty, onions, more cheese, and second bread.
Butter outsides of sandwiches and grill 3–4 minutes per side until golden and melty.
Slice and serve hot with extra sauce.
