01 - Preheat oven to 350°F.
02 - Pat chicken pieces dry and season all sides generously with salt and freshly ground black pepper.
03 - Heat olive oil and 1 tablespoon butter in a large Dutch oven or ovenproof casserole over medium-high heat. Sear chicken in batches until golden on both sides, about 3–4 minutes per side. Set browned pieces aside.
04 - Melt remaining tablespoon butter in the same pot. Add onions, carrots, and garlic, sautéing for 4–5 minutes until aromatic and softened. Sprinkle flour over the vegetables and cook for 1 additional minute, stirring continuously.
05 - Deglaze the pot with Calvados if using, followed by dry cider. Scrape up any browned bits from the bottom to incorporate flavor.
06 - Pour in chicken stock, then return browned chicken pieces to the pot. Layer apple slices over the top and add bay leaf and sprigs of fresh thyme.
07 - Bring to a gentle simmer. Cover and transfer to the oven. Bake for 50 minutes.
08 - Uncover, stir in heavy cream, and bake uncovered for a further 10–15 minutes until the sauce is slightly thickened and the chicken is tender.
09 - Remove and discard bay leaf and thyme sprigs. Taste the sauce and adjust seasoning if necessary.
10 - Serve hot, garnished with additional fresh thyme if desired.