Prepare:
Prepare artichokes for cooking by cutting the stem down to the base of the artichoke and cutting the top of the artichoke off to expose the inner leaves, as seen in the picture. Holding the artichoke by the base, smash it down on the counter a couple of times to open up the leaves. Sprinkle sea salt over the artichoke and then drizzle with olive oil. First salt, then olive oil so that the oil will transport the salt deep into the artichoke.
Microwave method:
Now put about 1/4 inch of water in the bottom of a microwave safe dish that is just large enough for the artichokes to fit snugly in on their bases. Cook on high in microwave for 15 minutes. Test for doneness by sticking a fork into the base, if it slides in easily they are ready. If not done in 15 minutes then cook in increments of 5 minutes until the fork test is passed. The outside leaves will become black.
BBQ method:
Put prepared artichokes on grill and cook until the fork test is passed. The outside leaves will be charred.
Wine pairing:
Watch Mark Oldman giving tips on pairing wine with artichokes here: http://youtu.be/kqsm65o4ch0. Generally, we pair a red like Tempranillo with grilled artichokes and a white like Verdelho with the microwaved artichokes.