Preheat the oven to 350 degrees . Butter a 9-by-13-inch baking dish.
In a saucepan, bring the salted water to a boil and add the grits. Reduce the heat to medium-low and cook, stirring often, until the grits are well thickened and partially cooked, 8 minutes. Remove the pan from the heat and stir in the butter and cheese. Let the grits cool slightly, then whisk in the egg yolks. Season the grits with cayenne, salt and pepper to taste.
Meanwhile, beat the egg whites until stiff. Gently fold the egg whites into the cooled grits. Pour the grits into the prepared casserole and bake for 30 minutes, until lightly golden and puffy.