Heat 1 tablespoon of vegetable oil in a large skillet over medium-high heat.
Add the thinly sliced onions and bell peppers to the skillet. Season with salt and pepper. Cook until they are soft and slightly caramelized, about 5 to 7 minutes. Remove from the skillet and set aside.
In the same skillet, add the remaining tablespoon of oil and the sliced beef steak. Season with salt and pepper. Cook until the steak is browned and cooked through, about 5 to 7 minutes.
Return the onions and peppers to the skillet with the steak, mix well and heat through.
Lay a tortilla flat and arrange two slices of provolone cheese on one half. Top with a quarter of the steak and vegetable mixture. Fold the tortilla over to cover the filling.
Heat a clean skillet over medium heat. Place the filled tortilla in the skillet. Cook until the tortilla is golden brown and crispy, about 3 minutes per side.
Repeat with the remaining tortillas and filling.
Cut each quesadilla into wedges and serve hot.