Grease a 2-quart rectangular baking dish; set aside.
In large saucepan, bring water to boiling. Stir in grits and salt. Reduce heat to medium-low. Cover and cook for 15 minutes or until very thick, stirring occasionally. Remove from heat. Stir in 1/2 cup of the cheese and the butter until melted. Set aside.
In large skillet, cook sausage until thoroughly cooked; drain off fat. Stir cooked sausage, milk, and eggs into grits mixture. Spoon into prepared dish.
Bake, uncovered, in a 350 degree F oven about 30 minutes or just until set. Sprinkle with remaining cheese. Bake, uncovered, about 5 minutes more or until cheese melts. Let stand 10 minutes before serving. Makes 8 servings.