Thank goodness for friends. After playing around with a couple of them last night with some really patient fellow foodies, we found a method that worked.
Cut off stem except for 1 inch, and any pointy tips of leaves.
Trim approximately 1 inch off the top.
Place in pot with water, lemon juice, 1 clove garlic, 2 bay leaves, and some salt.
Weigh down the artichokes by placing a steamer basket (those flying saucer things) upside down over the veggies.
Boil for 25-45 min.
Dip leaves in melted butter and scrape clean with your teeth.
The inner most leaves can be discarded, and all thistle-y parts should be as well.
The heart can be dipped in sauce, or saved to throw in a later salad.
What sauce? Well, that's up to you. Some swore by ranch, others mayo with lemon juice. I personally like a mild vinagrette.