Bring water and milk to boil in a large saucepan; add grits, and cook, stirring often, 5 minutes or until thickened. Stir in cheese, salt, and pepper; remove from heat.
Stir about one-fourth of grits mixture gradually into beaten eggs; add to remaining grits mixture, stirring constantly.
Spoon hot grits mixture evenly over hot Barbecue Pot Pie mixture. Bake at 425° for 15 minutes.