In an ovenproof casserole or dutch oven, brown the veal loin and kidneys over a moderate heat, turning frequently. Season with salt and pepper. Add the chopped onions, shallots, carrots, and wine to the casserole and bring to a boil. Reduce heat to a simmer, cover, and cook for 2 hours, turning the meat occasionally. After 1 1/2 hours, melt 1 tablespoon of the butter in a skillet and sautÄ the pearl onions until golden. Add a pinch of salt and enough water to half cover the onions and bring to a boil. Boil until all the water evaporates, shaking the pan occasionally. Melt the remaining butter in a large frying pan and cook the mushrooms until golden, about 15 minutes. Season with salt and pepper. Carve the veal loins and place them on a warmed serving platter with the kidneys. Spoon the mushrooms and onions around the meat. Strain the cooking liquid from the veal and spoon it over the meat and vegetables.
