Sprinkle chicken pieces with salt and pepper, then dredge both sides in flour.  Melt butter in a pot over medium-high heat. In two batches, brown chicken on both sides and remove to a clean plate.  In the same pot, add diced onion, carrots, and celery. Stir and cook for 3 to 4 minutes over medium-low heat. Stir in ground thyme and turmeric, then pour in chicken broth and apple cider. Stir to combine, then add browned chicken. Cover pot and simmer for 20 minutes.  While chicken is simmering, make the dough for the dumplings: sift together all dry ingredients, then add half-and-half, stirring gently to combine. Set aside.  Remove chicken from pot and set aside on a plate. Use two forks to remove chicken from the bone. Shred, then add chicken to the pot. Pour heavy cream into the pot and stir to combine.  Drop tablespoons of dumpling dough into the simmering pot. Add minced parsley if using. Cover pot halfway and continue to simmer for 15 minutes. Check seasonings; add salt if needed. Allow to sit for 10 minutes before serving. *Adapted from Gourmet Magazine