Plunge the crawfish/lobster in boiling salted water. When the crawfish/lobster no longer moves, remove them from the pot and split them into two halves on a plate, using a large knife.
Place each half on a heated oiled grill and cook for 12 minutes. Turn once or twice during cooking.
Mix the remaining ingredients together and baste the crawfish/lobster halves and continue cooking for 10 more minutes. Continue to baste as you turn and cook halves.
Just before serving time, bring sauce to a low boil for one minute, stirring continuously.
Serve lobster/crawfish halves with sauce in dipping container on the side.