Preheat oven to 350.Lighly grease a 2½ quart casserole dish.Bring water and salt to a boil in a large saucpan, then stir in grits and cook according to package directions.When grits are done, remove from heat.Stir in cheese and butter until melted.Stir in half-and-half.Add a couple of tablespoons of the hot grits to the lightly beaten eggs, stirring in one tablespoon at a time.Add egg mix to the pot of grits.Pour grits into prepared dish.Bake for 30-40 minutes until set.