In a large skillet over medium heat, heat 1 tablespoon oil. Add peppers and onions and season with salt. Cook, stirring often, until caramelized, 10-15 minutes.
Remove onions and peppers from skillet and set aside. Add the remaining olive oil and cook the steak until it has almost reached your preferred doneness. Season with salt and pepper.
Return veggies to the skillet and toss to combine with steak. Blanket the mixture with provolone cheese and cook covered, 3 minutes more, or until the cheese is melted. Divide the mixture amongst your hoagie rolls and serve.