Preheat the oven to 350 degrees F (180 degrees C). Heat the oil in a nonstick skillet set over medium-high heat. Season the chicken with the salt and pepper; add to the skillet in batches and brown all over.
Transfer the chicken to a 10 cup (2.5 L) casserole dish. Scatter the mushrooms, carrot and onion over top. Stir the sauce with the wine and drizzle over the casserole. (Casserole can be prepared up to this point and reserved, tightly covered in the refrigerator, for up to 1 day.)
Bake, covered, for 30 minutes; uncover and bake for 30 minutes or until chicken is tender and vegetables are cooked through. Meanwhile, prepare the noodles according to package directions. Arrange the noodles in a large serving bowl and spoon over the chicken, vegetables and sauce. Garnish with parsley and Parmesan (if using).