Place a large nonstick skillet coated with cooking spray over medium-high heat until hot. Add shredded carrot and onions; sauté 5 minutes or until tender. Sprinkle 2 tablespoons shredded cheese over each of 4 tortillas, and divide carrot mixture evenly over tortillas. Top each tortilla with 1/2 cup chicken, 2 tablespoons cilantro leaves, and 2 tablespoons cheese, and top with a tortilla.
Place skillet coated with cooking spray over medium heat until hot. Add 1 quesadilla, and cook 2 minutes on each side or until quesadilla is browned. Repeat with the remaining quesadillas. Cut each quesadilla into 6 wedges. Arrange 4 quesadilla wedges on each of 6 plates. Top each serving with 2/3 cup Fruit Salsa and about 3 tablespoons Avocado Cream.