Start by melting the butter in a skillet over medium heat. Add the chopped onion and minced garlic, stirring as they release their delicious aromas. Sauté until the onion is soft and translucent, about 2-3 minutes.

Sprinkle in the flour, stirring continuously. You don’t want any lumps! Cook for another minute or two until the flour takes on a light, golden color.

Slowly pour in the beef broth and milk, whisking the mixture to avoid clumps. Keep stirring until it thickens into a smooth, creamy gravy. Add a pinch of salt and pepper to bring out the flavors.

Gently fold the roast beef slices into the gravy, making sure they’re well coated. Reduce the heat and simmer for 5 minutes until the meat is heated through.

While the beef warms up, butter your bun halves and toast them. You can use a toaster, grill pan, or oven. Lightly golden buns will add a perfect crunch.

Pile the hot beef mixture onto the bottom half of each toasted bun. Lay a slice of cheese on top so it melts into the beefy goodness. Complete the sandwich by adding your preferred toppings and closing it up with the other bun half.

Serve the sandwiches immediately while the cheese is gooey and the buns are warm. Pair them with a side salad or crispy fries for the ultimate meal.