Heat a 12-inch cast-iron skillet over medium-high heat; add 2 tablespoons of the oil. Add the onions, green peppers and some salt and pepper and cook until the onions are browned and the peppers are tender, about 5 minutes. Add the garlic and cook 1 minute more. Remove to a bowl and set aside.
Return the skillet to medium-high heat; add 2 tablespoons of oil and the steak. Cook until browned on both sides, about 3 minutes. Remove to a bowl and set aside.
Wipe out the skillet and add the remaining 2 tablespoons oil. Place the pizza dough in the skillet and carefully stretch it out until it fills the entire skillet (the skillet will be hot). Add the steak, onion mixture, mozzarella and provolone over the top. Bake until the crust is cooked and the cheese is melted and browned, 15 to 20 minutes. Top with the chopped cherry or banana peppers if using.