Have your butcher joint the hare for you, halving the legs at the thigh, leaving the front whole and cutting the saddle into 4 pieces. Trim off the belly flaps.
Season the pieces of hare with salt and pepper. Heat a film of sunflower oil in a heavy-based flameproof casserole. Put in the hare pieces and brown slowly on all sides. Remove to a colander to drain.
Add the mirepoix to the casserole and cook until softened and browned. Return the hare pieces to the pot. Dust lightly with flour and cook for 2-3 minutes, stirring and turning the hare and vegetables. Pour in the wine, bring to the boil and reduce until almost completely evaporated. Add enough brown stock to cover the hare pieces and put in the bouquet garni. Bring back to the boil, skimming off any impurities. Cover the casserole with greaseproof paper and then the lid. Transfer to the oven to braise for 1½ hours.
Remove the hare pieces from the casserole and cool slightly, then pick the meat off the bones, keeping the pieces as large as possible. Put the meat in a heavy-based pan. Strain in just enough of the cooking liquid to cover. (The left-over liquid is heaven - use it as a game stock for a lentil and hare soup or another game dish.) Set aside.
To cook the polenta, bring 1.5 litres of water to the boil in a large saucepan. Add the garlic, thyme and 1 teaspoon salt. Stirring the water constantly with a whisk, gradually rain in the polenta. When all has been added, reduce the heat to very low and cook gently for 20-30 minutes, stirring frequently with a wooden spoon. The polenta is ready when it comes away from the side of the pan.
About 10 minutes before the polenta has finished cooking, reheat the braised hare and check the seasoning.
Add the Parmesan and mascarpone to the polenta and stir until smooth. Ladle the braised hare into deep soup plates and spoon the polenta on top.