In a large skillet, melt 1 tablespoon of unsalted butter with a splash of olive oil over medium heat. Add the thinly sliced yellow onions and sauté them slowly for about 12-15 minutes until they turn golden brown. Remove them from heat.

Wipe the skillet clean, pour in 2 cups of low-sodium beef broth, add 1 tablespoon of Worcestershire sauce and soy sauce, 2 cloves of minced garlic, and 1 teaspoon of fresh thyme. Simmer for about 5 minutes. Season to taste with salt and pepper, strain it into a bowl, and keep warm.

Lay out four slices of crusty French bread and layer with Swiss cheese, thinly sliced roast beef, caramelized onions, and top with another slice of Swiss cheese.

Heat a skillet or griddle over medium heat, butter the outer sides of the sandwiches, and grill for about 3-4 minutes on each side until golden and the cheese melts.

Remove sandwiches from the skillet, let them cool for a minute, slice in half, and serve immediately with warm au jus on the side.