Soak kidneys for at least 1 hour. Put 2 tablespoons of butter in flakes on a plate and place in the freezer. Peel shallots, cut them in half lengthwise and cut them into strips. Wash the thyme, dab dry, put some aside for garnishing.
Dab kidneys dry with kitchen paper and cut into wide strips. Heat the oil in a casserole or roasting pan, fry the kidneys thoroughly all around, remove.
Add 1 tablespoon butter and turnip greens to the cooking fat. Let it caramelize slightly while stirring. Sweat shallots and thyme in it. Season with salt and pepper, deglaze with vinegar, reduce slightly, add veal stock.
Add the kidneys and simmer until the sauce has boiled down by about half. Stir in ice cold butter flakes and thicken the sauce slightly. Season to taste with salt and pepper. Spätzle are delicious with it.