Preparation

1. Put on a large pot of water to boil to cook the artichokes. Fill a large bowl half way with cold water and add a squeeze of lemon juice. Trim the artichokes, cutting off the base of the stem, the small leaves around the base, and the tip of the cone. Place each trimmed artichoke in the lemon water as you work to prevent browning of the cut edges.
2. Place the artichokes in the pot of boiling water and cook until the stems are easily pierced with a knife, about 20 minutes. Drain the artichokes and pat dry with a kitchen towel. Cut each artichoke in half, vertically. Place, cut side down, on the towel until you are ready to grill them.
3. Make the aioli: Place the mayonnaise in a small bowl, and add the garlic, olive oil, parmesan and lemon zest; stir and reserve.
4. Preheat the grill on high. When hot, brush each artichoke on both sides with olive oil. Place on the grill, cut side down, and cook until the artichokes are browned and hot, 2–3 minutes. Serve immediately with aioli for dipping.