For the dumplings:
Preheat the oven to 200ºC/gas 6. Carefully remove the breasts from the pheasants and set aside. Bone the thighs and finely chop or mince the meat. Chop the thigh bones and drumsticks, dust with the flour and place in an oiled roasting tray with the onion and carrot. Roast for about 20–30 minutes, stirring every so often until the bones are lightly browned.
Transfer the roasted bones and vegetables to a saucepan. Gradually stir in the cider and chicken stock, then add the thyme and juniper berries. Bring to the boil, lower the heat and simmer gently for about 40 minutes.
To make the dumplings, roughly chop the chestnuts. Melt the butter in a small pan and gently cook the shallots with the chopped thyme for 2–3 minutes until softened. Transfer to a bowl. Add the chopped or minced thigh meat, chestnuts, breadcrumbs and parsley. Season with salt and pepper and mix well. Divide into four portions and shape into balls, then carefully wrap them in a couple of layers of caul fat.
Season the pheasant breasts and wrap them in a single layer of caul fat. Heat a little oil in a medium roasting tray in the oven, then add the dumplings and roast for about 15–20 minutes, turning them every so often. Add the pheasant breasts and roast for about 4–5 minutes on each side, keeping them nice and pink. (Don't be tempted to leave them in the oven to keep warm while you prepare everything else.)
Meanwhile, strain the sauce through a fine sieve into a clean pan and simmer over a medium heat until reduced and thickened to the desired consistency.
To serve, cut the pheasant breasts in half and arrange on warm plates with the dumplings. Pour the sauce over and serve with vegetables of your choice.