Toss the crawfish tails with the salt and cayenne pepper in a medium-size mixing bowl.

Heat the olive oil in a 3-quart saucepan over medium heat. Add the onions and cook, stirring, until slightly soft, about 2 minutes. Add the crawfish and garlic and cook, stirring, for 2 minutes. Add the stock and half-and-half and bring the mixture to a boil. Reduce the heat to medium-low and simmer for 2 minutes. Add the grits and stir constantly until they are tender and creamy, about 10 minutes. Add the cheese and stir to mix and melt it. Serve warm.