Only veal kidneys have a special finesse. There are, as far as I know (Ali Bab’s stuffed and braised fantasy apart), only three ways to prepare them. Whole, a thin layer of their fat is left surrounding them and they are cooked in a covered casserole either over low heat or in a medium oven, turned regularly, for from 40 to 45 minutes. To be grilled or sautéed, their fat and the thin protective membrane should be first removed; they are then split lengthwise and the fat pared out of the heart. Rub the halves in olive oil for grilling, season and grill first on the cut side for a couple of minutes, turn them, and, as soon as tiny pearls of blood appear at the surface, remove them.
A simple, classic recipe for sautéed veal kidneys is given in The French Menu Cookbook. For a rapid, sauceless sauté, try them à la Provençale, the split halves sliced crosswise more thinly (about inch thicknesses) than for a regular sauté, tossed rapidly, seasoned, in a heavy pan over high heat in butter, olive oil, or a combination. After a minute’s tossing add a handful of mixed finely chopped parsley and garlic (or mix the parsley with garlic pounded to a purée for a more delicate flavor), toss for another minute, sprinkle over lemon juice, and serve . . . Croutons are a welcome garnish.