Remove fat, membranes and cores from kidneys. Wash them and pat dry. Cut into thin slices and dredge lightly with flour.
Lightly brown the garlic in the oil, add the kidney pieces, and sauté quickly until browned on the outside. Take care not to overcook or kidneys will be tough. Season with salt and pepper to taste.
Mash the anchovies with the butter until they make a paste. Add this to the kidneys and stir well. When butter is melted, remove the pan from the heat, stir in the lemon juice, and sprinkle with the parsley.