In a large skillet over medium heat, melt 2 tablespoons of unsalted butter and 1 tablespoon of olive oil. Add 2 thinly sliced yellow onions, stirring frequently for 12-15 minutes until they turn golden and soft. Transfer them to a plate and set aside.

In the same skillet, combine 2 cups of beef broth, 1 tablespoon of Worcestershire sauce, 1 tablespoon of soy sauce, 2 minced garlic cloves, and a few sprigs of fresh thyme. Simmer for about 5 minutes and season with salt and black pepper to taste.

Lay out 4 slices of crusty French bread. For each sandwich, layer a slice of Swiss cheese, a generous portion of deli roast beef, half of the caramelized onions, and another slice of cheese. Top with another slice of bread.

Spread a thin layer of unsalted butter on the outside of each sandwich.

Preheat a skillet over medium heat and grill the sandwiches for 3-4 minutes on each side until golden brown and cheese melts.

Slice each sandwich in half diagonally and serve immediately with the warm au jus on the side.