Step one is popping them in the largest pot you have that will fit your pieces right after you cut the bottom of the stems off (only take a quarter of an inch off - the stem center is VERY edible!). Some directions will tell you to carefully cut the tip off of every single leaf - this is a ridiculous waste of time designed to make these seem harder to make than they are and to protect some special people from possibly poking a finger after they are cooked. If you are special, by all means cut off the tips.
Fill water to just cover the veggies, add some salt and garlic or whatever mild savory spice you'd like to the water for extra flavor. Boil the water until you can easily pull an inner (near the top center) leaf out with a gentle tug. This seems to take between 20 - 40 min depending on how many we are cooking. If you were not grilling these would be ready to serve. Grilling is an extra flavor step not a cooking step.
Take your cooked whole artichokes and slice them in half with a large sharp knife.
Spray the exposed center area with oil. We hit them with an olive oil mist, but if you like some other oil flavor go with whatever sounds good. Artichokes are a natural flavor enhancer, they contain a very unique chemical that makes whatever they are paired with taste slightly sweet and rich - keep that in mind when choosing spices and oils to match them up with.
Put these out on an already hot grill for about 5 minutes, give them a quarter turn to the right or left and let grill for about 3 or 4 more minutes and they are ready to eat!
We serve these with a simple lemon butter dip. [Simply take a few tablespoons - more or less depending on how many chokes you are serving - earth balance and squeeze half a lemon into it. Heat while stirring. When its melted, its done!]
These pair up well with all sorts of summer food, on this day they went well with marinated, grilled mushrooms.
One quick side note for anyone who might be like I was: You eat a grilled (or otherwise) whole artichoke by peeling off each leaf, dipping the end that was attached to the stalk in the butter and scraping the soft white "meat" off on your teeth. Keep working your way to the heart and the soft white part gets bigger and bigger until you can eat almost the whole leaf. Stop when you reach the inner purple leaves! Take a spoon and gently scrape the purple leaves and the hairy spines off of the heart. The entire heart and the clear-ish center of the whole stem is very edible and supper yummy in the butter sauce. Enjoy it - its worth the "work" of eating it!