1. To make the cinnamon apples, add the chopped apples, brown sugar, cinnamon, nutmeg and lemon juice to a pan. Stir together until apples are well coated.
2. Cook apples on medium heat until at desired tenderness, about 10 minutes. Set aside to cool to about room temperature.
3. To make the filling, beat the cream cheese, brown sugar and cinnamon together in a large mixer bowl until smooth.
4. Add the milk and beat until smooth. Set cream cheese mixture aside and make the whipped cream.
5. Add heavy whipping cream, vanilla and powdered sugar to a large mixer bowl and whip on high speed until stiff peaks form. Set aside 1 1/2 cups of whipped cream.
6. Carefully fold the remaining whipped cream into the cream cheese mixture into two parts, folding until well combined.
7. To layer the dessert, use a 9 inch square pan. Add a full layer of graham crackers to the bottom of the pan, breaking some into smaller pieces to fill in gaps as needed.
8. Add about half of the filling on top of the graham crackers and spread into an even layer.
9. Add about half of the cooled apples on top of the filling in an even layer and gently press into the filling.
10. Repeat with another layer of graham crackers, then filling, then remaining apples.
11. Add one additional layer of graham crackers on top.
12. Spread the remaining whipped cream that was set aside earlier onto the top of the graham crackers.
13. Refrigerate until firm, 4-5 hours.
14. Top the icebox cake with crushed graham crackers or crushed apple chips, then cut into pieces and serve.