Opinions on this differ, but I steam artichokes with the base side up. I can’t believe that I still haven’t bought a vegetable steamer, but…I haven’t, and this seems to work just fine. Cover, with just enough room for some steam to escape, and steam in approximately 3/4 inch of water on low heat for 40-50 minutes (depending on size of artichoke). If the water boils down too low and gets kinda brown, just add a little more. When the base is fork-tender, they’re ready.
Eat
