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.
Recipe adapted from Emeril's Creole Christmas, by Emeril Lagasse, published by William Morrow