Have your butcher bone the saddles of rabbit, to yield 4 fillets. Ask him to chop the bones (which you want for the sauce).
To make the stuffing for the rabbit, take the black pudding from its skin and put into a food processor with the cream. Blend to a soft, spoonable consistency. Transfer to a bowl. Coarsely chop the rabbit livers and kidneys, and sauté in a little hot oil with the shallot and garlic just to sear and brown. Add the thyme for the last few seconds. Add the warm liver and kidney mixture to the black pudding and fold together. Check the seasoning.
For the root vegetable and wild mushroom juice, heat a little oil in a saucepan. Add the mirepoix and rabbit bones (plus any vegetable and garlic trimmings) and cook to a good rich brown. Add the wine and boil until almost all evaporated. Pour in enough stock or water to cover the bones and vegetables. Bring to the boil and simmer for 15 minutes, skimming regularly (if you skim constantly, you will end up with a beautifully clear liquid, not a cloudy one). Strain, preferably through a sieve lined with muslin. Keep this juice warm.
To cook the rabbit, brush the packets on all sides with oil, then put into a hot cast-iron frying pan that has an ovenproof handle. Cook over a moderate to low heat to sear to a golden brown on all sides. Transfer to the hot oven and cook for 5-8 minutes. Remove and leave to rest in a warm place while you finish the other components of the dish.
To finish the root vegetable and mushroom juice, heat a film of oil in a frying pan until very hot, then add the carrot and parsnip cubes and the sliced mushrooms and toss for 2½-3 minutes. Drain on kitchen paper, then add to the warm juice. Check the seasoning.
For the spinach, toss the leaves in a hot pan until they are wilted and juices are exuded. Drain well and season. Keep hot.
To serve, cut each rabbit packet into three slices. Set three cornmeal cakes on each plate, pile spinach on top and arrange the rabbit on the spinach. Add all the juices from the rabbit to the root vegetable and mushroom juice, and spoon over the rabbit.