Put the olive oil and water in a large pot and bring to simmer. Meanwhile, prepare artichokes.
Cut off the stems close to the base. Pull off the tough, lower petals. Cut off the top inch of the artichoke. Trim off the thorny tips of outer petals with kitchen shears.
Place artichokes in simmering pot, bottoms up. Cover and simmer 30 minutes. Artichokes are done when a knife inserted in the base meets no resistance.
To eat, pull off leaves, squeeze with a little lemon (if desired) and dip in melted butter. Scrape off the tender part of the leaf with your front teeth. When you reach the center, remove the prickly purple leaves and the fluffy thistle layer that covers the disc-shaped and delicious artichoke heart.
For smaller portions, cut the steamed artichokes in half and remove the prickles and fluff before serving.