To prepare the sauce, heat oil in a medium saucepan over medium heat. Add carrot and onion; saute 10 minutes or until soft. Add flour; cook 1 minute. Combine carrot mixture, milk, and broth in blender; process until smooth. Return mixture to pan, and add mushrooms, sherry, salt, and pepper. Cook until reduced to 3 1/2 cups (about 30 minutes), stirring occasionally.
Preheat oven to 350°.
Place a large nonstick skillet coated with cooking spray over medium-high heat. Add the chicken; cook 5 minutes on each side or until done. Cut chicken into thin slices; keep warm.
Combine 2 cups sauce, the spaghetti, and chopped parsley in a large bowl. Spoon into a 13 x 9-inch baking dish coated with cooking spray. Arrange chicken on top of spaghetti mixture; spoon remaining sauce over chicken. Sprinkle with breadcrumbs and cheese. Bake at 350° for 15 minutes or until top is lightly browned.