The important thing to remember when working with cardoons is that just like their cousin the artichoke, they turn brown when cut and exposed to air. To clean them, strip the leaves and use a sharp peeler to remove any thick, stringy parts on the outside, cut them into lengths and then strips, and plunge them immediately in cool water that had been acidulated with a few generous squeezes of lemon juice. I toss the lemon halves right into the water. Keep the cut cardoons immersed while you clean the rest. You can transfer them to clean boiling water, or just cook them right in the acidulated water for a bit of tang in the final flavor.