Heat olive oil in a large skillet over medium-high heat. Add the steak slices and cook until browned, about 2-3 minutes per side. Remove from skillet and set aside.
In the same skillet, add the onion and bell pepper, seasoning with salt and pepper. Sauté until vegetables are tender, about 5 minutes.
Return the steak to the skillet with the vegetables, mixing well.
Lay out the tortillas on a flat surface. Sprinkle half of each tortilla with the mozzarella and provolone cheeses.
Divide the steak and vegetable mixture evenly among the tortillas, placing it on top of the cheese. Fold the tortillas in half over the filling.
Wipe the skillet clean and return to medium heat. Cook each quesadilla until golden brown and crispy on both sides, about 3 minutes per side.