Trim artichokes: Cut the bottom inch of thorny leaves off each artichoke. Remove any small, discolored leaves around the sides and closer to the stem; they’re not going to taste good. Use a vegetable peeler to remove the outer layer of the stem. Cut each artichoke in half through the stem, heart, and leaves. If you’d like, you can rub the cut parts of each artichoke with one lemon half to limit browning.