In a small bowl, stir together mustard, mayonnaise, barbecue sauce, and hot sauce.
Store, covered, in refrigerator up to 3 days.
In a large bowl, combine ground beef, Worcestershire, salt, and pepper.
Shape ground beef into 6 oval patties.
In a medium cast-iron skillet, over medium hat, melt 2 tablespoons butter.
Add onion; cook, stirring occasionally, until onion is soft and golden brown, approximately 35 minutes.
In a large cast-iron skillet, cook patties over medium-high heat until browned and cooked through, approximately 2 minutes per side.
Remove skillet from heat; remove patties from skillet; wipe out skillet.
Layer 1 bread slice with 1 tablespoon Secret Sauce, 2 to 3 tablespoons caramelized onions, 1 slice cheese, 1 patty, and another 1 tablespoon Secret Sauce.
Top with another bread slice; repeat with remaining bread, Secret Sauce, caramelized onions, cheese, and patties.
Heat skillet over medium-high heat; melt 2 tablespoons butter in skillet.
Working in batches, cook sandwiches, flipping once, until golden brown and heated through, approximately 3 minutes per side.
Add remaining butter to skillet as needed.
