Cut off stem and with a sharp knife trim the base so artichokes sit flat. Make a cut across the top of the leaves, parallel to the base. With scissors, trim the leaves so they have straight edges.
To cook conventionally, bring a large shallow pan of salted water to a boil. Submerge artichokes, cover tops with a heat proof heavy plate to keep them submerged and cook for 35 to 45 minutes or until a leaf in middle can be pulled out easily. Drain them upside down so water runs out.
To cook in microwave, wrap each one individually in microwavable plastic wrap and set them in a round plate. Microwave for 10 minutes or until a center leaf can be pulled out easily. Remove plastic wrap (carefully; it will be hot).
Serve as is, with each person pulling out a leaf and dipping it in melted butter, or remove cone of dinner leaves in one fell swoop and reserve them for later. With a small spoon scoop out choke. Replace cone of leaves, upside down and serve with melted butter seasoned with lemon or vinaigrette.