Combine grits, water and salt in a saucepan.
Cook over medium heat until slightly thick.
Add butter and cheese.
Stir over low heat until both are melted.
Break egg into a measuring cup; add enough milk to make 2/3 cup.
Stir egg mixture into grits and mix well.
Pour into a greased 13x9x2 inch baking dish.
Bake in a 350°F oven 20 minutes, watching carefully, or until golden brown.
Allow to stand 10 to 15 minutes to thicken.