Prepare chestnuts, or use canned ones. Cut pheasants into pieces as you would a chicken. Sauté pieces in a chunk of butter and oil until lightly browned. Pour Armagnac over them and set aflame. When flame dies, remove pheasant from skillet.
Add carrots and onions to skillet and sauté until browned. Stir in the flour and cook 1 minute. Add thyme. Tie bay leaves and parsley into a bundle (bouquet garni) and add to skillet. Add garlic, salt, and pepper. Pour in wine and stir until sauce thickens. Add onions and return pheasant to the skillet. Set lid ajar and simmer about 40 minutes.
Cut stems off even with mushroom caps and wash. Add mushrooms and cooked chestnuts. Sauté diced salt pork in a piece of butter. Add to skillet. Simmer 30 minutes, or until pheasant is tender. Prepare recipe of boiled potatoes. When pheasant is done, taste and adjust seasonings and thickness of sauce with beurre manié). Arrange pheasant on platter. Add onions, mushrooms, and whole boiled potatoes. Spoon sauce over pheasant and garnish with slices of truffle.