In a large skillet over medium heat, heat 1 tablespoon oil. Add peppers and onion and season with salt. Cook, stirring often, until caramelized, 12 to 15 minutes.

Remove onions and peppers from skillet and set aside. Add remaining tablespoon oil and cook steak until it has almost reached your preferred doneness, about 5 minutes. Season with salt and pepper.

Return veggies to skillet and toss to combine with steak. Blanket mixture with provolone and cook, covered, until the cheese is melted, about 3 minutes more. Divide mixture among hoagie rolls and serve.