Trimming artichokes can be a long, painful process, but it doesn't have to be. Here's how I learned to do it many years ago from a friend who had been a line cook at Commanders Palace in New Orleans, where they go through thousands of hearts every brunch.
1. Fill a bowl with cool water and add the juice of 1 lemon. Hold an artichoke in one hand with the stem facing toward you and the tip facing away. Slowly turn the artichoke against the sharp edge of a knife while making an abbreviated sawing motion, cutting the outer leaves at the base.
2. Keep trimming until you've cut away enough of the tough leaves so you can see only light green at the bases. Cut away about the top half-inch of the artichoke tip and dip the artichoke into the lemon water so the cut surfaces don't get discolored.
3. With a paring knife, trim away the very tip of the stem, then peel the stem and base of the artichoke, going from the tip to where the base meets the leaves. You'll have to do this at least five or six times to make it all the way around the artichoke. When you're done, there should be no dark green tough spots left, only pale green and ivory.
4. Cut each artichoke into lengthwise quarters, and if there is a fuzzy choke inside, cut just below the choke to the very base of the leaves and the choke will pop off, leaving a clean heart below. If you want the heart to remain whole, use a grapefruit spoon to dig out the fuzz. Place the artichoke in the lemon water and go on to the next artichoke.