Mix first 3 ingredients and 1 tablespoon cilantro in large bowl.
Add shrimp; toss to coat. Let stand 10 minutes.
Prepare barbecue (medium-high heat) or preheat broiler.
Remove shrimp from marinade. Skewer 6 shrimp on each of 2 skewers. Skewer onions on remaining skewer.
Season shrimp and onions with some of marinade.
Grill onions until tender and cooked through, about 3 minutes per side.
Add shrimp to grill; cook until pink, about 2 minutes per side.
Coarsely chop onions. Remove shrimp from skewers; divide between plates.
Bring marinade to boil. Mix in onions, cheese and remaining 1 1/2 tablespoons cilantro.
Spoon onion mixture over shrimp.