01 - In a large skillet over medium heat, melt 1 tablespoon of butter with olive oil. Add sliced onions and sauté, stirring frequently, until deeply caramelized and golden brown, about 12 to 15 minutes. Transfer onions to a plate and set aside.
02 - Wipe the skillet clean. In a small saucepan, combine beef broth, Worcestershire sauce, soy sauce, minced garlic, and thyme. Bring mixture to a gentle simmer for 5 minutes. Season with salt and pepper. Strain through a small strainer and keep warm.
03 - Arrange 4 bread slices on a work surface. Layer each with 1 slice Swiss cheese, a generous portion of roast beef, caramelized onions, and a second slice of Swiss cheese. Cover each with remaining bread slices.
04 - Spread unsalted butter evenly on the outsides of each sandwich.
05 - Heat a clean skillet or griddle over medium heat. Grill sandwiches for 3 to 4 minutes per side, pressing gently, until bread is crisp and golden and cheese is melted.
06 - Slice sandwiches in half and serve immediately with warm au jus for dipping.