Sprinkle steak with salt and pepper. Heat a medium, heavy skillet over medium-high until hot. Cook steak, turning once, until browned on both sides but still pink inside, 2-3 minutes per side. Transfer to a cutting board and set aside.
In same skillet, heat 1 tbsp. oil over medium. Add red and yellow bell peppers, onions, and cook, stirring until softened, 6-8 minutes. Add mushrooms and cook until softened, about 3 minutes more. Set aside.
Lay 4 tortillas on a flat surface, and divide steak and vegetables between them. Top with cheese and remaining tortillas.
In a large nonstick skillet heat remaining 1 tbsp. oil over medium. Cook 1 quesadilla at a time, flipping once, until golden brown on both sides, about 3 minutes per side.