If using a grill that needs to be started ahead of time, prepare the fire.
Fill a stockpot with water — deep enough to for the artichokes to fully float — and bring to a boil.
Trim the ends off the artichoke stems and slice the artichokes in half lengthwise. Set them, cut side down, on a platter or cutting board.
Zest the lemon and reserve the zest. Slice the lemon in half. Crush the garlic.
When the water is boiling, squeeze the lemons and drop the rinds into the water. Add the salt, pepper and garlic. Gently lower the artichoke halves into the boiling water and lower the heat to simmer. Cook until the leaves pull away when gently tugged, 15 to 20 minutes, turning the artichokes over halfway through.
Remove the artichokes with tongs and drain on a towel. When cool enough to handle, remove and discard the fuzzy choke and brush the cut side with olive oil. Place them cut-side down on the grill and cook about 3 minutes, until grill-marks form.
Serve the artichokes on a platter with melted butter or aioli.