01 - Preheat oven to 350°F. Pat chicken pieces thoroughly dry and season generously on all sides with salt and pepper.
02 - In a large Dutch oven or ovenproof casserole, heat olive oil and 1 tbsp butter over medium-high heat. Brown chicken on both sides in batches, about 3-4 minutes per side; set aside.
03 - Add remaining butter to the same pot. Sauté onions, carrots, and garlic for 4-5 minutes until softened. Sprinkle with flour and cook 1 minute more.
04 - Deglaze with Calvados if using, then add cider. Stir thoroughly, scraping any browned bits from the bottom of the pot.
05 - Add chicken stock and return browned chicken pieces to the pot. Add apple slices, bay leaf, and thyme sprigs.
06 - Bring to a simmer, cover, transfer to oven, and bake for 50 minutes.
07 - Uncover, stir in heavy cream, and bake uncovered for another 10-15 minutes until the sauce thickens slightly and chicken is tender.
08 - Remove bay leaf and thyme sprigs. Taste and adjust seasoning. Serve hot, garnished with additional thyme if desired.