Preheat the oven to 350 degrees Fahrenheit.

In a large skillet, heat olive oil over medium high heat. Once the oil is hot, add the onion and saute 5-8 minutes or until the onion has wilted and has started to turn a light golden brown. 

Add the leftover pot roast to the skillet along with 1/2 cup of the cooking liquid (or beef broth). Reduce heat to low and simmer while you make the au jus. 

Heat the remaining cooking liquid (or beef broth) in a small pot over medium high heat until it begins to simmer. Add the soy sauce and simmer an additional 2-3 minutes before removing from heat. 

Remove the meat mixture from heat to begin sandwich assembly. 

To assemble, open the buns and spread both sides with a thin layer of butter. Cut the slices of provolone in half, layer two half slices on the bottom bun, followed by leftover roast/onion mixture, then two more half slices of cheese. Close the sandwiches and wrap with foil. 

Place the foil-wrapped sandwiches on the top oven rack and bake for 7-10 minutes or until the cheese is deliciously melty. Serve with small dishes of au jus for dipping and your favorite side. Enjoy!