Preheat oven to 350°.
Bring water and salt to a boil in a medium saucepan. Gradually add grits, stirring constantly. Cover and simmer 8 minutes or until thick, stirring frequently. Remove pan from heat. Add 1 cup cheese and butter, stirring until cheese melts.
Combine milk and next 3 ingredients (milk through eggs), stirring with a whisk. Stir milk mixture into grits mixture. Pour into an 8-inch square baking dish coated with cooking spray. Bake, uncovered, at 350° for 45 minutes. Sprinkle with 1/2 cup cheese; bake an additional 15 minutes or until cheese melts. Let grits stand for 10 minutes before serving.