Pour the beef broth into a large skillet and stir in the Worcestershire sauce, garlic powder, and onion powder. Bring to a gentle simmer over medium heat.

Add the roast beef slices to the hot broth, separating them as they go in. Warm for 1-2 minutes, just until hot.

Butter the cut sides of the hoagie rolls and toast cut-side down in a hot skillet until golden.

Lift the warm beef out of the broth with tongs, let the extra drip off, and pile it high onto the toasted rolls.

Lay two slices of provolone over the hot beef on each sandwich, close the rolls, and let the cheese melt for a minute.

Ladle the hot broth into small cups and serve alongside for dipping.