Stack cutlets and cut crosswise in half, then cut each stack lengthwise into matchstick-size pieces. Heat 1 tablespoon oil in 12-inch nonstick skillet over high heat; stir-fry pork for 2 minutes or until no longer pink. Remove from skillet with slotted spoon. Salt to taste.
Add 1 tablespoon olive oil to skillet. Add mushrooms and onions and stir-fry for 1-2 minutes or until crisp-tender. Remove from skillet and wipe skillet clean with paper towels.
Assemble quesadillas, sprinkle 1/4 cup cheese over half of each tortilla. Top each with pork and mushroom mixture. Sprinkle each with 1/4 cup remaining cheese. Fold tortilla in half and press gently.
Add 1 tablespoon oil to skillet. Cook quesadillas, 2 at a time, over medium heat for 2-4 minutes or until golden brown, turning once. Remove from skillet and cover with aluminum foil to keep warm. Repeat with remaining tortillas.