Braising keeps this lean wild turkey meat moist and flavorful. Serve this dish as a first course, and this Roasted Wild Turkey Breast with Fall Vegetables recipe as a main course.
Combine wine, port, and thyme in a large pot and reduce by half over high heat. Add demi-glace, chicken stock, bay leaves, peppercorns, garlic, parsley, carrots, celery, and onion, and bring to a boil. Reduce heat so liquid is simmering, add turkey legs whole, with feet if still attached.
Cover and cook gently until meat easily separates from bone when pricked with a fork, about 2 hours for a young bird. Older birds can take up to 4–5 hours. Check every half hour. If, during cooking, pan juices get lower than 1 inch in the pot, add stock or water to bring level back up. When meat is cooked, remove and let cool.
Strain cooking liquid into a saucepan, pressing solids with a wooden spoon or spatula to extract all juices. Bring to a boil over high heat and reduce by half. Season to taste with salt and pepper, then stir in butter, if using. Keep hot.
Bring a large pot of salted water to a boil. Add pasta and cook until al dente. Drain and divide among 4–6 plates.
While pasta cooks, remove turkey meat from bones and tendons, and shred. Place on top of cooked pasta, then spoon on sauce. Garnish plates with parsley sprigs and serve at once.