I never knew how to eat a whole artichoke until 2 months ago. I have to say, it's a good experience. After cooking it in some fashion, you pluck off the outer leaves and scrape off the fleshy inside part of the leaf with your teeth (don't try to eat the whole leaf -- it's really fibrous). The closer you get to the middle, the more tender the leaves become. Kind of like a veggie cinnamon roll...the inside is always the best. As you continue to pluck off leaves, the anticipation grows as you get closer to the heart, and finally! you're there. You pry off the the "choke" (the spiky part that you don't want to go down your throat) and you get to the best part of the artichoke.
There are different ways of cooking artichokes. The first time I made them, I baked them and dipped them into a balsamic vinegar mayo dip. It was good, but I felt like the dip over-powered the artichoke flavor. The second time around, I boiled and then grilled them, using a lemon-garlic marinade. They were delicious. If you're confused about how to eat an artichoke, this is a good resource. I got the following recipe from allrecipes.com. All I did was cut back on some of the oil because it seemed like too much. So, go ahead, you're equipped with knowledge and recipes...try a whole artichoke!
2 large artichokes
1 lemon, quartered
1/4 cup olive oil
4 cloves garlic, chopped
1 teaspoon salt
1/2 teaspoon ground black pepper
1. Snip off the ends of the leaves where there's a little spike (see the above link for the complete list of "How To Eat an Artichoke"). Fill a large bowl with cold water. Squeeze the juice from one lemon wedge into the water. Trim the tops from the artichokes, then cut in half lengthwise, and place halves into the bowl of lemon water to prevent them from turning brown.
2. Bring a large pot of water to a boil. Meanwhile, preheat an outdoor grill for medium-high heat.
3. Add artichokes to boiling water, and cook for about 15 minutes. Drain. Squeeze the remaining lemon wedges into a medium bowl. Stir in the olive oil and garlic, and season with salt and pepper.
4. Brush the artichokes with a coating of the garlic dip, and place them on the preheated grill. Grill the artichokes for 5 to 10 minutes, basting with dip and turning frequently, until the tips are a little charred. Serve immediately with the remaining dip.
If you don't feel like grilling them, they also work well boiled and then broiled in the oven.