In large mixing bowl, whisk eggs until light and fluffy. Whisk in milk, ¾ teaspoon cinnamon and nutmeg. Stir in apples. Pour mixture into pie crust; place on baking sheet.
In medium mixing bowl, combine flour, brown sugar, and remaining ½ teaspoon cinnamon. Cut in butter using a pastry blender or fork. Sprinkle over apple mixture.
Bake in a preheated 400°F oven 10 minutes. Reduce heat to 350°F and continue baking until apples are tender and crust is golden brown (about 40 minutes).
Remove from oven and allow to cool 2 hours. Refrigerate until ready to serve.