Preheat oven to 350°. Bring milk just to a boil in a large saucepan over medium-high heat; gradually whisk in butter and grits. Reduce heat, and simmer, whisking constantly, 5 to 7 minutes or until grits are done. Remove from heat.
Stir in egg and next 3 ingredients. Pour into a lightly greased 11- x 7-inch baking dish. Sprinkle with grated Parmesan cheese.
Bake, covered, at 350° for 35 to 40 minutes or until mixture is set. Serve immediately.