Preheat oven to 375°F.
Combine sugar and corn starch in medium bowl. Whisk in eggs. Stir in butter, corn syrup, milk and vanilla. Fold in half of apples. Pour into pie crust.
Place remaining apples in overlapping circle on top of pie. Sprinkle brown sugar cinnamon mixture on top of apples. Bake for 50 minutes or until center of pie is set. Cool on wire rack. Refrigerate.
In a small bowl mixture together brown sugar, cinnamon and nutmeg.