Chop the carrot and onion into large pieces (no need to make it fancy, you will remove them from the broth later). In a large pot, boil the turkey necks, onion, and carrots for 60-90 minutes, or until the turkey meat falls off the neck bone.
Remove turkey necks from the broth and set aside. Drain the broth through a colander to remove the chunks of onion and carrots.
Place turkey necks and broth back into the large soup pot. Add in rice and let it simmer on low for about 20 minutes.
Once the rice is cooked, add in the diced potato. Let the soup simmer until all ingredients are fully cooked. Season with salt and pepper to taste. Serve hot with a sprinkling of fresh dill and green onion.