Preheat skillet over medium heat. Heat tortillas for 1 minute each side. Remove tortillas from skillet and cover with towel to keep warm.
Combine both cheeses in a small bowl. Layer warm tortillas with half the cheese, half the steak slices and half the mushrooms. Add remaining half of cheese and top with other tortilla. Over medium heat, warm 2 teaspoons of corn oil in skillet then add quesadilla. Lightly brush top with remaining 2 teaspoons of corn oil. Cook 5 minutes or until bottom is light brown. Turn over and brown other side. Cut into 4 or 6 wedges. Serve with sour cream and salsa on side.