Melt the butter in a skillet and cook the onion over medium heat for 10 to 12 minutes until soft and golden.
Put the onion, cooking liquid, broth, Worcestershire, thyme and pepper in a saucepan. Bring to a simmer and cook for 5 minutes.
Add the cooked roast slices to the jus. Cover and reheat over medium-low heat, turning gently, until the center of the meat reaches 165°F throughout. Allow approximately 10–15 minutes for refrigerated, sliced or shredded beef; the thermometer reading determines when it is ready.
Serve immediately, or transfer the hot beef, onions and jus to a preheated slow cooker set to warm for holding at 140°F or above.
Split and toast the rolls. Add provolone, if using, and return them briefly to the broiler just until the cheese melts.
Fill each roll with drained beef and onions. Strain or ladle the hot jus into six small bowls and serve one beside each sandwich.
