1. To prepare pistou, combine first 7 ingredients in a food processor; pulse until finely chopped. Let stand 10 minutes.
2. Prepare grill.
3. To prepare grouper, sprinkle fish evenly with salt and pepper. Place fish on grill rack coated with cooking spray; grill 4 minutes on each side or until fish flakes easily when tested with a fork. Serve with pistou.
Wine note: Soellner Wogenrain Grüner Veltliner 2006 ($16) from Austria boasts herbal and green pea aromas that pair well with the fresh, green flavors of this dish. The wine's bright, mouthwatering acidity slices through the olive oil and brings out the lime zest. —Jeffery Lindenmuth