01 -
Melt butter in a skillet over medium heat. Add diced onions and minced garlic, cooking until softened and fragrant, about 5 minutes.
02 -
Sprinkle flour over the softened onions and garlic. Stir continuously for 2-3 minutes until the flour turns golden, forming a roux to thicken the gravy.
03 -
Gradually pour in beef broth and milk while stirring to prevent lumps. Continue cooking and stirring until the gravy thickens and coats the back of a spoon, approximately 5 minutes.
04 -
Add the sliced roast beef into the gravy, stirring gently to coat each piece. Simmer just until heated through and tender, about 3-4 minutes.
05 -
Butter the interior of the sandwich buns. Toast them on a griddle or under a broiler until golden and crisp, about 2-3 minutes.
06 -
Fill each toasted bun with the hot beef and gravy mixture. Top immediately with slices of provolone or Swiss cheese to allow melting. Add optional lettuce and tomato if desired.
07 -
Serve sandwiches hot with extra gravy on the side for dipping and pickles or chips if preferred.