A wonderful sign of spring, asparagus is at its best between March and May. Choose spears with bright green stalks and purple-tinted tips. If you do not plan to cook the asparagus immediately, stand the spears upright in a pan filled with 1 inch of water and refrigerate. Peeling the ends of the asparagus stems is optional, although it makes for an attractive presentation. If you are using thick asparagus, peeling removes the tough outer part and makes the entire stalk more uniform to ensure even cooking.