Place the beef in the freezer for 20 to 30 minutes to make slicing easier.
Heat 2 tablespoons of vegetable oil in a large, deep sauté pan over medium-low heat. Add the onion and bell peppers, cooking slowly and stirring occasionally until the vegetables are very tender. Reduce the heat if they begin to brown. Stir occasionally while preparing the steak.
Take the beef from the freezer and set it on a cutting board. Use a sharp knife to trim away excess fat and slice the beef thinly against the grain. Chop the slices into very small pieces, continuing until the pieces are about ¼-inch in size.
Once the vegetables are softened, transfer them to a dish and return the skillet to the stove. Add more oil as needed and heat the skillet over medium-high heat. Add half of the chopped steak, stirring frequently for 4 to 5 minutes, until fully cooked and no pink remains. Season this batch with ¾ teaspoon of seasoned salt and ½ teaspoon of garlic pepper. Use a slotted spoon to transfer the cooked steak to the dish with the peppers and onions, leaving the juices behind. Repeat the process with the remaining steak, seasoning, and additional oil as necessary.
Preheat the oven to 400°F.
Spread the softened butter onto the inside of the hoagie rolls. Arrange them on a baking sheet and bake for 3 to 5 minutes until lightly toasted and golden.
Drain any excess juices from the pan and return it to the stove. Combine the cooked steak, peppers, and onions back into the pan. Place the provolone cheese slices in a circle on top of the mixture, cover the pan, and allow the cheese to melt over medium heat for about 4 to 5 minutes. Stir to mix the melted cheese into the filling.
Use tongs to scoop the filling onto the toasted hoagie rolls. Serve immediately for an irresistible sandwich experience.