I learned this very simple technique from my mom and I have always wondered if anyone else used this method. I have never done the whole french trimming/ water with lemon juice and flour thing.
I always do a few at a time as they have a very long shelf life once cooked this way.
I cut to about 1" the bottom stems of the artichokes. i put them in a pot so they fit tightly standing up.Pour in about 1" of water and another 1/2" or so of cider vinegar. Add a tight fitting cover and bring to a boil,turn down and simmer about 45 minutes until a large leaf pulls out easily and the 'meat' comes off easily when you skin it with your teeth. all done. the acid of the vinegar makes it so you really don't need a dipping sauce, (though i was raised dipping them in a mustard mayo mixture)
warning: i have burned more pots than i can tell you because I forgot them and they ran out of liquid, so check your liquid level after 20 minutes and add more as needed. my mom used to do this with a pressure cooker but i've never had one.