In a flameproof casserole, heat the fat until sizzling. Season the pigeons, put them in the casserole and seal on all sides. Lower the heat, add the shallots, garlic and thyme, cover the casserole and cook for 20–30 minutes, until tender. Tip out the excess fat, pour in the armagnac, quickly replace the lid and cook for 1 minute.
Transfer the pigeon to a serving