We dont really eat enough of these. Maybe because we think they are a bother to prepare. A large one would probably take about an hour to cook. (I dont bother to do the 'cheffy' thing and cut off the leaf tips.) You could leave the stalks on though, as they help you turn the artichoke while it's cooking. (Remove them before serving.)
All you do is just put them in boiling salted or acidulated water and boil them until the outside (bottom) leaves come away very easily.
I let mine get cool, (or you can leave them in the fridge - probably for about a week and they would be ok) - serve them with a good vinaigrette (see recipe list). When you get down to the hairy choke - cut or pull this off and discard. The heart of the artichoke is absolutely delicious dipped in your lovely vinaigrette. Simple!