In a small bowl, combine salt, black pepper, and paprika to create the seasoning blend. Set aside. Thinly slice the beef steak against the grain to ensure tenderness. Slice the onion, mushrooms, and green pepper into uniform strips for even cooking.

Heat butter in a large skillet over medium-high heat. Once melted, add the sliced onions, mushrooms, and green peppers. Sauté, stirring occasionally, until the vegetables soften and become slightly caramelized, or until they reach your preferred level of tenderness. Remove from the skillet and cover with foil to keep warm.

In the same skillet, increase the heat to high and add olive oil. Once the oil is hot, spread the thinly sliced steak evenly across the pan. Allow it to sear undisturbed for a minute or two until it starts to brown but remains slightly pink in the center.

Flip the steak and sprinkle with half of the prepared seasoning mix. Stir in the minced garlic, ensuring it evenly coats the meat. Return the sautéed vegetables to the pan and mix everything together. Season with the remaining spice blend, stirring to distribute the flavors throughout.

Lower the heat to medium, evenly distribute the provolone cheese over the steak and vegetable mixture, and cover the skillet with a lid. Allow the cheese to melt, enveloping the mixture in a rich, creamy layer.

While the cheese is melting, lightly toast the hoagie rolls to add a crisp texture. If desired, spread a layer of mayo on the inside of each roll. Once the cheese has melted, divide the steak and vegetable mixture between the two hoagies, stuffing them generously.

Serve immediately while warm, letting the melted cheese and juicy steak create a mouthwatering bite. Pair with crispy fries, a side salad, or pickles for a complete meal.