Cook noodles according to package directions and drain in a colander; do not rinse.
Spray an 8- or 9-inch square ovenproof baking dish with cooking spray. Spread tomato sauce evenly on bottom. Spoon noodles on top and compress with hands. Sprinkle half of cheese over noodles.
Preheat oven to 400°F. In a large skillet, heat oil over medium heat. Add onion, carrot and celery and cook, stirring occasionally, until softened, about 5 minutes. Add turkey and cook, breaking up with a wooden spoon; cook until meat is crumbly, 4 to 5 minutes. Add flour and stir for 2 minutes. Stir in half-and-half and bring to a boil. Reduce heat and simmer, stirring often, until mixture is thick and creamy, 4 to 5 minutes. Season with salt and pepper, stir in parsley and spoon mixture evenly on top of noodles. Sprinkle remaining cheese on top.
Bake until casserole is hot and top is golden brown, about 20 minutes. Let stand for 10 minutes before cutting. Serve with extra sauce.