1. Preheat the oven to 350°F (175°C).
2. Heat the butter and olive oil in a large skillet over medium heat. Add the shallot and garlic and cook until softened, about 3 minutes.
3. Add the cognac and flambé. Once the flame has died down, add the chicken stock, white wine, thyme and rosemary. Simmer for 5 minutes.
4. Add the chestnuts and cream and simmer for another 3 minutes.
5. Season the partridge inside and out with salt and pepper. Place it in a roasting pan and pour the sauce over it.
6. Roast the partridge for 25-30 minutes, basting frequently with the sauce.
7. Serve the partridge with a ragout of mushrooms, truffles, and shallots.