2 lemons, halved
6 large artichokes
2/3 cup extra-virgin olive oil
1/3 cup fresh lemon juice
3 tablespoons chopped fresh mint
Squeeze juice from halved lemons into large bowl filled with cold water. Cut stem off 1 artichoke, leaving about 1 inch. Snap off outer 2 rows of leaves. Cut off top 1/3 of artichoke. Quarter artichoke lengthwise. Using small knife, cut out choke and prickly small leaves. Place artichoke in lemon water. Repeat with remaining artichokes.
Bring large pot of salted water to boil. Drain artichokes, add to pot, and boil until crisp-tender, about 15 minutes. Drain. Transfer artichokes to rack and cool. (Can be prepared 1 day ahead. Cover and refrigerate.)
Prepare barbecue (medium-high heat). Whisk oil, 1/3 cup lemon juice, and mint in small bowl. Season dressing to taste with salt and pepper. Brush artichokes with dressing. Grill until tender and lightly charred in spots, turning occasionally, about 8 minutes. Transfer artichokes to platter. Drizzle with some of remaining dressing. Serve warm or at room temperature.