Heat your grill to high. I like to grill these over hardwood charcoal. But a gas grill will work.
Grill Artichokes starting cut side down for about 2-3 minutes each side until nice grill marks form. These can take a lot of grilling, so don't be afraid if the leaves start to char up. The Artichoke meat will still be fine. I typically grill mine for 6-10 minutes at 650 degrees.
Remove from grill, plate, and serve with a side of the BBQ Aioli for dipping.