Make the Au Jus:

1. In a large skillet, melt the butter over medium heat. Add sliced onion and cook until they begin to brown slightly.
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4. Add sugar, garlic, thyme, and bay leaves to the skillet and continue cooking until the onions are a deep golden color, about 15 minutes.
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7. Add the wine and simmer until the liquid is nearly gone.
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10. Pour in the broth, Balsamic vinegar, and Worcestershire sauce and bring to a boil. Reduce heat to a simmer and let reduce by half, so that about 2 1/2 cups of liquid remain. This takes about 30 minutes. Pour the Jus through a strainer set over a saucepan. Taste and season with salt and pepper.
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Prepare the Roast Beef:

1. Preheat the oven to 325° F.
2. Heat the oil in an ovenproof skillet over medium-high heat. Season the beef with salt and pepper and sear for a few minutes on each side until browned.
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4. Add butter, garlic, and thyme, spooning the melted butter over the meat until well coated.
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6. Place skillet in the heated oven and roast for 25 minutes, spooning the butter over the meat a few times during the cooking process.
7. Remove skillet from oven and transfer the roast beef to a cooling rack set over a baking sheet. Let beef rest for 20 minutes before slicing very thin.

Assemble the sandwiches:

1. Heat oven to 425°.
2. Slice the French bread in half horizontally. Lay bread halves on a baking sheet and spread each sandwich with a thin layer of mustard. Arrange the sliced roast beef on the bread and then top with sliced provolone. Place the top half of the bread onto the sandwich and brush the outside with the melted butter.
3. Transfer the baking sheet to the hot oven and place another baking sheet on top of the sandwiches and weigh it down with a heavy skillet. Bake for about 5 minutes or until cheese is melted.
4. Reheat the Au Jus and serve immediately.