Preheat oven to 350°F. Lightly grease a 9x13-inch baking dish.
Warm olive oil and 1 tbsp butter in a large skillet over medium heat.
Sauté onions and peppers until softened and lightly golden, about 6–8 minutes.
Stir in mushrooms and cook 2–3 minutes more. Add garlic and cook 30 seconds. Transfer vegetables to a plate.
Increase heat to medium-high. Sear the sliced beef in batches until just browned, 2–3 minutes.
Season beef with salt and pepper. Splash in Worcestershire and toss with the cooked vegetables. Remove from heat.
Slice the rolls horizontally to keep tops and bottoms intact. Place bottoms in the baking dish. Spread with mayonnaise if using.
Layer half the provolone over the roll bottoms. Pile on the beef-and-veggie mixture, then top with remaining provolone.
Cap with roll tops. Mix melted butter, garlic powder, parsley, and sesame seeds. Brush all over the tops.
Cover with foil and bake 12 minutes. Uncover and bake 5–8 minutes, until cheese melts and tops are golden.
Rest 5 minutes. Slice along the seams and serve warm.