Preheat your oven to 375°F (190°C). Lightly spread softened butter on the cut sides of the rolls. Place rolls cut-side up on a baking sheet and toast in the oven 5–7 minutes until lightly golden. Remove and set aside.

Warm roast beef

In a sauté pan over medium heat add 1 tablespoon olive oil. Add the sliced roast beef in a single layer just to warm through, about 1–2 minutes. If using thicker leftover roast, slice thinly and briefly warm until heated but not overcooked. Transfer warmed beef to a plate and cover to keep warm.

Assemble sandwiches

Divide warmed roast beef evenly among the toasted roll bottoms. Pile the mushroom-onion mixture (see Mushroom topping directions) over the beef, then top with 2 slices of provolone cheese per sandwich. Place the sandwich tops on and return assembled open sandwiches to the oven (or under a broiler) just until the cheese melts, about 2–3 minutes. Watch carefully to avoid burning the bread.

Mushroom topping

Heat a large skillet over medium-high heat. Add 1 tablespoon unsalted butter. When melted and foaming, add the sliced mushrooms and sliced onion. Cook, stirring occasionally, until mushrooms release their liquid and it evaporates and onions are soft and beginning to caramelize, about 8–10 minutes.

Add the minced garlic and thyme and cook another 30–60 seconds until fragrant. Season with salt and black pepper. Remove from heat and keep warm until ready to assemble sandwiches.

Au jus

In a small saucepan over medium heat combine the beef broth, wine (if using), soy sauce or Worcestershire, beef base (if using), garlic powder, and onion powder. Bring to a gentle simmer.

In a small bowl whisk the cornstarch into the cold water to make a slurry. Gradually whisk 1/4 of the hot broth into the slurry to temper, then stir the slurry back into the saucepan. Simmer 2–3 minutes until slightly thickened. Taste and adjust seasoning with salt, pepper, or an extra splash of soy/Worcestershire. Keep warm; transfer to small bowls for dipping when serving.

Garnish / serving

Place each assembled sandwich on a plate. Sprinkle chopped parsley over the mushrooms and optionally a pinch of hot pepper flakes. Serve immediately with a small bowl of warm au jus for dipping.