Heat oil in a large pan. Add sliced onion and a pinch of salt. Cover and cook for 5 minutes until onion is soft and slightly transparent. Stir in hot sauce and beef broth, then remove from heat. Season with salt.

Heat a large pan. Spread butter on one side of each bread slice. Cook buttered side down until toasted, about 2 minutes. Transfer toasts to a plate. Cook bacon in the same pan until crisp, about 4 minutes per side. Drain on paper towels. Wipe the pan clean.

Season beef patties with salt. Cook on a griddle over medium-high heat until medium-rare, about 2 minutes per side. Top each patty with a slice of Emborg Natural Havarti Slices and cook, covered, until melted, about 1 minute.

Place burgers on the untoasted sides of 4 toasts. Top with bacon, onion, and sweet barbecue sauce. Close the burgers and serve, with extra barbecue sauce on the side.

MAKE AHEAD

The onion can be stored in the refrigerator overnight and gently reheated before serving.