Slice one of the lemons in half and keep close to rub all cuts of the artichoke with the lemon juice.
Cut off the top inch of each artichoke & trim the tips of each of the leaves. Trim the bottom of the stem.
Cut the artichokes in half & with a spoon scoop out the thistle. Rinse under cold water and rub with the lemon.
Steam the Artichokes
Slice the other lemon and place in a large pot with about 3 inches of water. Bring to a boil.
Arrange the artichoke halves in a steamer basket and suspend over the water. Cover and reduce heat. Steam for about 15 minutes. While the artichokes steam, prepare the aioli.
Lemon Garlic Aioli
Mince the garlic and place in a small bowl with the olive oil, egg, salt, pepper and chopped garlic. Juice the lemon into the mix.
With an immersion blender, place the blade over the egg yolk and blend. Hold the blade over the yolk for 30 seconds, then slowly move the blender through the mix to emulsify.
Cover and refrigerate.
Grill the Artichokes
Drizzle the steamed artichokes with oil and sprinkle with salt and pepper.
Grill the artichokes face down on medium heat for 8-10 minutes.
Remove from the heat and serve with the aioli and a lemon wedge.