Fill a large bowl with cold water. Squeeze the juice from one lemon wedge into the water. Trim each leaf with scissors, then cut an inch off the top and stem, cut in half lengthwise, and quickly place halves into the bowl of lemon water to prevent them from turning brown.
Bring a large pot of water (or two) to a boil. Meanwhile, preheat an outdoor grill for medium-high heat.
Add artichokes to boiling water, and cook uncovered for about 15-20 minutes–til a leaf pulls out easily. While they’re cooking, make a marinade from remaining lemon, olive oil, garlic, salt and pepper.
Drain artichokes, brush with marinade, and place them on preheated grill (outer sides down at first to hold in the liquid). Grill the artichokes for 5 minutes each side, basting with sauce until the tips are a little charred. Serve immediately with the remaining sauce for dipping. Prepare to die of deliciousness.
TIP: You can also boil, marinate and freeze them. Then later, defrost, BBQ and enjoy!