Stew: Pat the chicken dry with paper towels, then season with salt and pepper. Heat 2 tsp of the oil in a large Dutch oven over medium-high heat until just smoking. Add half of the chicken, skin side down, and cook until golden on both sides, about 10 minutes. Transfer the chicken to a plate and remove the skin. Pour off the chicken fat and reserve. Return the pot to medium-high heat and repeat with the remaining two tsp oil and the remaining chicken. Pour off and reserve the chicken fat in the pot.
Add the butter to the dutch oven, and melt over medium-high heat. Add the mirepoix or the carrots, celery and onion and 1/4 tsp salt and cook until softenened, about 7 minutes. Stir in the Wondra or flour and cook for about a minute, or until it smells slightly nutty and browns a little. Whisk in the sherry, scraping the bottom to incorporate browned bits. Stir in the broth, half and half, thyme and bay leaves. Nestle the chicken, with any juices, into the pot. Cover and simmer until the chicken is fully cooked and tender, about an hour.
Transfer the chicken to a cutting board. Discard the bay leaves. Allow the sauce to settle for a few minutes, then skim the fat from the top. Shred the chicken, discarding the bones and return it to the stew.
Dumplings: Stir the flour, baking powder and salt together. Microwave the milk and fat in a bowl until warm, about a minute. Add the milk mixture to the flour mixture, stirring well until incorporated. Drop by golf ball sized spoonfuls into the simmering stew and cover. Cook without lifting the lid until the dumplings are steamed and double in size, about 15 minutes. Serve hot.