1. Cut the top quarter off each squash; reserve tops. Discard seeds. Arrange squashes, cut sides down, in 2 (11 x 7-inch) baking dishes. Fill each dish with 1-inch of water; microwave 1 dish at HIGH 15 minutes. Remove dish; repeat with remaining dish. Cool.
2. Preheat oven to 350°.
3. Heat a large skillet over medium-high heat. Coat pan with cooking spray. Add sausage; sauté 5 minutes or until browned, stirring to crumble. Remove sausage with a slotted spoon. Add carrot, onion, and garlic to drippings in pan; sauté 2 minutes, stirring frequently. Stir in 1/2 cup water; bring to a boil. Reduce heat to medium; cover and cook 8 minutes or until carrot is tender.
4. Combine sausage, carrot mixture, quinoa, parsley, thyme, salt, and pepper; stir in 1/2 cup cheese. Stuff about 1 cup quinoa mixture in each squash, and top each serving with 1 tablespoon cheese. Arrange stuffed squashes in a broiler-safe baking dish, and place tops in dish. Bake at 350° for 20 minutes or until thoroughly heated. Remove from oven.
5. Preheat broiler to high.
6. Broil squashes 4 minutes or until cheese is golden.