How to Make It
Fill a large bowl with water and squeeze in the lemon halves. Using a paring knife, trim the artichoke stems. Using a serrated knife, cut off the top thirds of the artichokes. Using scissors, cut off the tips from the remaining leaves to remove the thorns. Cut the artichokes in half lengthwise and scoop out the furry choke. Add the artichokes to the lemon water.
Fill a large saucepan with 1 inch of water and bring to a boil. Add the artichokes cut sides down, cover and simmer over moderate heat until tender, about 10 minutes. Transfer the artichokes to a plate and let cool.
Light a grill or preheat a grill pan. In a medium bowl, mix the mayonnaise with the lemon zest, lemon juice, garlic, mustard, parsley and oregano and season with salt and pepper.
Rub the artichokes with the olive oil and season with salt and pepper. Grill them over moderately high heat, turning once, until charred in spots, about 6 minutes. Transfer to plates and serve with the dipping sauce.