1Peel the artichokes and slice paper-thin with a knife or mandoline. Heat the butter to foaming in a sauté pan, add the artichoke slices, and season with salt and pepper. Sauté until they start softening and browning but still have a little bite, just over five minutes.
2Pour over the oil and heat through gently, then remove from the heat and stir in the walnuts and dill. Squeeze on lemon juice to taste and adjust the seasonings. Serve warm or at room temperature.