Preheat the oven to 200C/400F/Gas 6.
Using a sharp knife, cut away the breasts from each pheasant and set the four breasts aside. Remove the legs from each pheasant, then cut the carcasses into several pieces. Place the pheasant legs and carcass pieces into a roasting tin.
Add the onion, tomatoes, thyme and bay leaves and roast in the oven for 15 minutes. Remove and place all of the roasted bones and vegetables into a large pan and cover with water. Place on the heat and bring to the boil. Reduce the heat and simmer for 45 minutes, skimming off any impurities that rise to the surface. Strain the stock into a separate pan and reserve. Discard the bones and vegetables.
Season the pheasant breasts with salt and freshly ground black pepper. Heat an ovenproof frying pan until hot, add the olive oil and the pheasant breasts. Fry the breasts for two minutes on each side, until golden-brown all over. Transfer to the oven and roast for 10-12 minutes, or until completely cooked through. Remove from the oven, place on a plate and rest for five minutes before carving.
Place the pan used to fry the pheasant breasts back onto the heat. Add the red wine and bring to the boil, stirring and scraping the bottom of the pan with a wooden spoon to release the browned bits. Cook the wine until the liquid volume has reduced by half.
Add the reserved pheasant stock and bring to the boil. Reduce the heat and simmer until the sauce has reduced and is thick enough to coat the back of a spoon. Season, to taste, with salt and freshly ground black pepper.
For the mash, pierce the chestnuts with a knife, making a small slit in the shell - this prevents them from exploding. Place the chestnuts into a baking tray and roast in the oven for 20-25 minutes until tender. Leave the chestnuts to cool, then peel and roughly chop.
Place the potatoes into a pan of salted water and bring to the boil. Reduce the heat and simmer for 12-15 minutes until the potatoes are tender. Drain and return to the pan, then place over the heat for one minute to drive off any excess moisture. Mash the potatoes well, then add the olive oil, chestnuts and flatleaf parsley. Mix well and season, to taste, with salt and freshly ground black pepper.
For the parsnips, place the parsnips, sherry and honey into a baking tray and mix to combine. Season with salt and freshly ground black pepper. Roast in the oven for 20 minutes, turning half way through, until the parsnips are tender and golden-brown.
To serve, spoon the mash into the centre of the plate and place a sliced pheasant breast on top. Place some parsnips alongside, then drizzle over the sauce.