Prep the Artichokes: Trim the tops and sharp ends of the leaves off the artichokes. Cut each artichoke in half lengthwise and scoop out the fuzzy choke in the center. Squeeze a bit of fresh lemon juice on them immediately to keep them from turning brown (or drop them into a bowl of lemon water if prepping ahead).
Boil: Bring a large pot of water to a boil. Add the artichokes and cook for about 15 minutes, then drain them well.
Grill and Serve: Preheat an outdoor grill to medium-high heat. In a small bowl, squeeze the remaining lemon wedges, stir in the olive oil, chopped garlic, salt, and black pepper. Brush the artichoke halves generously with the garlic-oil mixture. Place them cut-side down on the grill for 5 to 10 minutes, turning and basting frequently until the tips have a light char. Serve immediately hot off the grill alongside the chilled remoulade.