In a mixing bowl, toss the crawfish tails with salt and cayenne. In a 3-quart saucepan, over medium heat, add the olive oil. When the oil is hot, add the onions. Season the onions with salt and cayenne. Saute for 2 minutes, or until the onions are soft. Add the crawfish and garlic. Continue to cook for 2 minutes. Add the stock and half and half to the pan. Season with salt and cayenne. Bring the liquid to a boil. Reduce the heat to medium-low and simmer for 2 minutes. Add the grits and stir constantly until they are very tender, about 10 minutes. Add the cheese and stir to mix and melt it. Serve warm.