Heat the oil in a heavy large frying pan over medium heat. Add the onion and garlic and saute until translucent, about 5 minutes. Add the carrot and celery and saute until the vegetables are tender, about 5 minutes. Add the turkey and saute 1 minute. Add the marinara sauce. Decrease the heat to medium-low and simmer gently for 15 minutes to allow the flavors to blend, stirring often. Stir in the basil. Season the sauce, to taste, with salt and pepper. (The sauce can be made 1 week ahead. Cool the sauce completely, then transfer it to a container and freeze for future use. Bring the sauce to a simmer before using.)
Meanwhile, cook the spaghetti in a large pot of boiling salted water until just tender but still firm to bite, stirring often, about 8 minutes. Drain, reserving 1 cup of the cooking liquid. Add the pasta to the sauce and toss to coat, adding enough reserved cooking liquid to moisten as needed. Serve with the Parmesan.