To remove possible strong flavors from the kidneys, soak them in water with a few drops of lemon juice or vinegar for about an hour for smaller kidneys, two hours for larger ones. Pour them into a colander and let them drain for a few minutes.
In large skillet, sauté the garlic cloves in olive oil over moderate heat until they are just turning brown around the edges. Remove and discard.
Raise the heat to high and add the sliced kidneys. Sauté them briskly, tossing them from time to time and seasoning with salt and pepper, then adding just a drizzle of white wine. If using, add the anchovy-butter paste at the very end and let it dissolve into the cooking juices.
Turn off the heat and mix in the minced parsley. Serve immediately, topped with more minced parsley, accompanied with buttered rice or mashed potatoes if you like.