Prepare barbecue (medium heat). Using scissors, cut off spiky tips from artichokes. Using spoon, scrape out chokes from centers. Wrap each artichoke in foil. Using tines of fork, poke holes in foil. Grill until leaves pull away easily from heart, turning occasionally, about 40 minutes. Unwrap artichokes. Discard any outer leaves that may be charred and any tough inner leaves. Arrange 6 artichokes on platter.
Remove leaves from remaining 2 artichokes and place on platter.
Transfer artichoke hearts to processor.
Add mint, cream cheese, and oil; blend until smooth. Season to taste with salt and pepper.
