In a large skillet, melt 1 tablespoon of unsalted butter with a drizzle of olive oil over medium heat. Add the thinly sliced yellow onions, stirring frequently for about 12-15 minutes until they become golden brown and deeply caramelized. Transfer to a plate and set aside.

In a clean saucepan, combine 2 cups of low-sodium beef broth, 1 tablespoon of Worcestershire sauce, 1 teaspoon of soy sauce, 1 minced garlic clove, and 1 teaspoon of fresh thyme. Heat over medium-low and let simmer for about 5 minutes, then season with salt and black pepper, and strain into a bowl.

Lay out 4 slices of crusty French bread. Place a slice of Swiss cheese on each, followed by roast beef and caramelized onions. Top each with another slice of cheese and cover with remaining bread.

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

Preheat a skillet over medium heat. Place the sandwiches on the griddle and cook for about 3-4 minutes on each side until golden brown.

Once golden and cheese is melted, remove sandwiches, slice in half, and serve with warm au jus.