Melt 2 tablespoons of butter in a skillet over medium-low heat. Add the onions and cook, stirring occasionally, for 20 minutes until they are a deep jammy brown. Stir in the balsamic vinegar in the last minute. Remove from the pan.

Shape the beef into 4 thin, rectangular patties to match the shape of your bread. Press the cracked peppercorns into both sides of the meat. In the same skillet over medium-high heat, sear the patties for 3 minutes per side until a crust forms.

Whisk together the mayo, ketchup, horseradish, Worcestershire, and paprika. This sauce is best if made 15 minutes ahead of time to allow the flavors to marry.

Spread softened butter on one side of each bread slice. Turn them over and spread a generous layer of the secret sauce on the non-buttered side.

Layer a slice of Gruyère, the beef patty, a heap of caramelized onions, and another slice of Gruyère between two pieces of bread (sauce-side in).

Griddle the sandwiches in the skillet over medium heat. Press down lightly with a spatula or a heavy weight. Toast until the bread is a deep mahogany gold and the Gruyère is cascading down the sides.