Heat a large nonstick skillet over medium-high heat. Coat pan with cooking spray. Add onion and jalapeño; sauté 2 minutes. Add mushrooms and salt; sauté 5 minutes or until moisture evaporates. Remove mushroom mixture from pan; keep warm.
Wipe pan clean with paper towels. Return pan to heat; add 1 tortilla. Cook 1 minute; turn tortilla over. Arrange about 1/3 cup mushroom mixture over half of tortilla; top with 1 tablespoon cheese. Fold in half; cook 30 seconds on each side or until cheese melts and tortilla is golden. Repeat procedure with remaining tortillas, mushroom mixture, and cheese. Cut each quesadilla into 4 wedges.