Here's how I make artichokes (and I make 'em all the time, as they are quite possibly the best veggie in the world...)
Cut just the end of the stem, and then cut the pointy part straight across about 1" from top. Then, with scissors, cut each leaf across (parallel to the bottom & top cuts) so you get rid of the sharp "hook". Then, in a large kettle of salted, rolling boiling water, place your artichokes in and then cover. Turn heat down, if the water boils over. I boil till the chokes are just fork tender in the stem.
Then...
drain thoroughly in a collander (turn them head down)
and place each in a bowl. (after all, nobody likes to share!)
Take each leaf off, and dip in melted butter. Scrape just the flesh &; about 1/3 of the way up with your teeth. Pure heaven. Discard leaves in your bowl.
When you reach the thin leaves, forget them. Put one hand on the stem half and one on the leaf half. Pull (think New Year's cracker) and you'll see the "choke". With a spoon, CAREFULLY take out just the thistle-looking stuff (this would be on the stem end). You will have a disc-shaped piece of heaven. Cut this into small pieces, and throw them in your leftover melted butter. (think soup) Eat these babies, and you will know why nobody shares.
Also, the part that's left (the leaf end) has what we used to call "the bite-around", which is a circle-shaped portion of the flesh that you can...well...bite around.
I want your input when you try these!
Also, you can eat these with a Garlic Aioli, which is good with either a hot artichoke or a cole artichoke, but in my opinion, it is best as made above.