Bring a large pot of water to a boil and squeeze the juice of 1 lemon into the water. Add artichokes and boil for 10 minutes. Drain and pat dry.
Meanwhile, in a small bowl, whisk together mayonnaise, lemon juice, lemon zest, capers, parsley, garlic, Weber® Roasted Garlic and Herb Seasoning, and ground white pepper. Cover and refrigerate until ready to serve.
Preheat grill to medium-high heat (375°F–400°F).
Brush artichokes with olive oil and season with Weber® Roasted Garlic and Herb Seasoning.
Place artichokes cut side down on the grill. Cook for 5–6 minutes, or until grill marks appear and the artichokes are tender. Remove from grill and let cool slightly.
Arrange artichokes on a serving platter and garnish with remaining lemon wedges. Sprinkle desire amount of Member's Mark™ Mediterranean Sea Salt Grinder over the artichokes. Serve with the lemon herb aioli on the side.