Divide the pasta dough into 4 equal portions. Using additional tapioca starch as needed to avoid sticking, roll out the dough to roughly ¼ inch thick. Use a pizza cutter or knife to cut noodles roughly ½ x 2 inches.
Boil the noodles for 7 minutes, drain, and rinse with cold water. Set aside.
In a large pot over medium heat, melt the ghee. Sauté the chicken pieces, carrots, onion, celery, and garlic until the chicken is browned and the vegetables are soft, about 5 minutes. Add the chicken broth and simmer until the chicken is cooked through, about 10 minutes. Reduce the heat to low, add the cooked noodles, and simmer for a few minutes to heat through. Season with salt and pepper.