Cut the legs from the pheasant using a sharp knife, then carefully remove the breasts. Place the legs, breasts and carcass in a cooking pot with the onion, leek, thyme, chicken stock and wine. Season lightly, bring to the boil, then lower the heat and simmer gently for 10 minutes.
Take out the pheasant breasts and set aside on a plate. Continue to simmer the soup for a further 20 minutes. Melt the butter in a small saucepan and stir in the flour over a low heat. Whisk the flour and butter mixture into the simmering soup in pieces to thicken it, then continue to simmer for another 20 minutes.
Meanwhile, preheat the oven to 200°C/gas 6. Score the chestnuts and place on a small baking tray. Cover with foil and bake for about 12–15 minutes, then remove to a plate and leave until cool enough to handle. Peel away the skins and cut each chestnut into two or three pieces.
Strain the soup through a fine sieve into a clean saucepan and add the cream. Remove the pheasant meat from the legs and cut the breast into bite-sized pieces. Add to the soup with the chestnuts, chanterelles and chopped parsley. Simmer gently for 5 minutes. Check the seasoning and serve.