Preheat oven to 375°. Bring 1 tsp. salt and 6 cups water to a boil in a large saucepan over medium-high heat. Gradually whisk in grits, and return to a boil. Reduce heat to medium-low, and cook, whisking often, 15 minutes or until thickened.
Remove grits from heat, and whisk in butter. Whisk about one-fourth of hot grits mixture into eggs; whisk egg mixture into remaining hot grits mixture. Gradually whisk in milk. Whisk in cornmeal and remaining 1/2 tsp. salt. Stir in cheese and ground red pepper. Pour grits mixture into a lightly greased 2 1/2-qt. baking dish.
Bake at 375° for 1 hour to 1 hour and 10 minutes or until golden brown and set.