Mix all sauce ingredients in a small bowl.
Chill the secret sauce while you prep patties.
Divide beef into 4 even portions.
Shape into thin, wide patties.
Season with salt and pepper.
Heat butter in a skillet over medium heat.
Add onions and cook until golden brown.
Remove onions and set aside.
Cook patties 3–4 minutes per side.
Remove and keep warm.
Wipe skillet clean and add more butter.
Lay out 4 bread slices.
Spread secret sauce on each slice.
Add cheese, onions, and one patty.
Top with more cheese and bread.
Grill sandwich until golden and crisp.
Flip and repeat on the other side.
Slice and serve with extra sauce.