Makes four 8-inch sandwiches
Position an oven rack in center of oven and preheat to 350 degrees.
Place broth, onion, carrot, and celery in a small pot and bring to a simmer. Turn heat to low and cover to keep warm.
Place a piece of parchment paper on a baking sheet and arrange bread slices, cut sides up, on sheet. Gently remove some of the soft inner part of the bread if it is too thick or dense, leaving about a 1/2-inch-thick shell. Spread 2 tablespoons Homemade Mustard along top and bottom of each sandwich. Place two slices provolone along the bottom side of each sandwich, followed by 6 ounces of roast beef. Drizzle a scant tablespoon broth over beef. Transfer to oven and cook until meat is just warmed through, about 6 minutes.
Remove from oven and spread 1/4 cup caramelized onions on top of meat; place sandwiches on serving plates. Carefully dip sandwiches on both sides into beef broth before serving or pour beef broth into four ramekins and serve with sandwiches for dipping.