In a large skillet, heat 1 tablespoon of unsalted butter combined with a drizzle of olive oil over medium heat. Add the sliced medium yellow onions and sauté them, stirring frequently for about 12-15 minutes, until they become deep golden brown and sweetly aromatic. Once caramelized, transfer the onions to a plate.

Using the same skillet, pour in 2 cups of low-sodium beef broth, followed by 1 tablespoon each of Worcestershire sauce and soy sauce, and 1 teaspoon of minced garlic. Stir in a few sprigs of fresh thyme and bring the mixture to a simmer. Let it cook for about 5 minutes; season with salt and black pepper to taste. After simmering, strain the au jus into a bowl.

Prepare your French Dip Grilled Cheese by laying out 4 slices of crusty French bread. On each slice, layer with thick slices of Swiss cheese, followed by a generous amount of thinly sliced roast beef, and top with caramelized onions. Add another slice of cheese on each stack before closing them off with the remaining slices of bread.

Gently spread unsalted butter on the outsides of each sandwich. This will help lock in the flavors and give your French Dip Grilled Cheese a delightful crunch when cooked.

Place the sandwiches in the skillet over medium heat and cook each side for about 3-4 minutes or until the bread turns a beautiful golden brown and the cheese inside is melted.

Slice the sandwiches in half diagonally and serve them immediately alongside the warm au jus for dipping.