Kidneys are strange creatures unless you are used to them! To prepare a whole pig or lamb kidney, you need to lay them flat, place your hand on top and, using a sharp knife, cut through the meat to split it, then remove the white "core" of hard fat using a sharp, pointed knife (your butcher will do this for you if you ask). Then place them in a water with a couple of tablespoons of red wine vinegar for at least ½ hour to cleanse the meat (otherwise, they can taste too strong). Rinse them quickly in cold water and pat them dry before cooking.
Veal kidneys, however, are different and have not had time to develop the white "core" of hard fat. You can either cook them whole or (for this recipe) cut each "lobe" of the kidney to separate them. You should have pieces about 1"-1½" (2.5 - 3.5cm) across so you can cut larger lobes in two if necessary.
Melt the butter in a pan until it turns golden (not brown). Lightly season the kidney pieces with salt and freshly ground pepper and add them to the pan. Leave them to brown on all sides for no more than 3 minutes, turning regularly. When cooked, kidneys should still be pink in the middle. Too much cooking makes them hard like bullets. After 3 minutes, remove the kidneys from the pan using a slotted spoon and put them aside at room temperature.
Add the whole baby onions to the pan and cook gently for about ten minutes to soften (Add a little butter to the pan if necessary). Meanwhile, slice the mushrooms. When the onions have softened add the lardons and mushrooms to the pan. Mix the Madeira with the cornflour (cornstarch), increase the heat in the pan and add the Madeira mix. Use a wooden spatula to 'deglaze' the pan. Continue to boil for a few minutes to reduce the sauce, then turn down the heat and add the cream plus salt and freshly ground pepper to taste. Simmer for a few more minutes to reduce the sauce further, until it has a "thick pouring" consistency. Add the kidneys back to the pan. Leave to reheat a few minutes then serve with Boiled Rice.