Warm a large skillet over medium-high heat and drizzle in some olive oil.
Add the sliced onions and green bell peppers to the skillet and cook, stirring occasionally, for 3 to 5 minutes until softened; toss in mushrooms if using and sauté for another 3 minutes.
Slide the cooked veggies to one side of the pan, crumble the ground beef in the empty space, and cook it through until browned and no longer pink, around 5 to 7 minutes.
Mix in garlic powder, Worcestershire sauce, salt, and black pepper, stirring well; cook together for about 2 minutes to blend the flavors.
Lower the heat, place a slice of provolone cheese on top of the beef mixture, cover the skillet and let it melt gently for 2 to 3 minutes.
While the cheese softens, carefully slice the hoagie rolls lengthwise, stopping before cutting all the way through.
Scoop the cheesy beef and veggie filling evenly into the prepared rolls.
Serve the sandwiches hot, optionally giving the rolls a quick toast beforehand for extra crunch.