Combine the first 7 ingredients in a small saucepan, and stir well. Prepare grill. Place saucepan containing barbecue sauce on grill rack. Place oysters on grill rack, and grill 5 minutes or until a few oysters begin to open. Remove oysters from heat. Carefully open oysters with an oyster knife, leaving on the half shell.
Sprinkle oysters with parsley, and drizzle with barbecue sauce. Serve with lemon wedges.