Begin by preparing the apple fries. Slice the apples into thin wedges and set aside.
In a shallow bowl, combine the flour, cinnamon, nutmeg, and salt. Mix well.
In another bowl, whisk together the eggs and milk until smooth.
Place the breadcrumbs in a third shallow bowl.
Dip each apple wedge first into the flour mixture, then into the egg mixture, and finally coat with breadcrumbs. Set aside on a plate.
In a large skillet, heat about 1 inch of vegetable oil over medium heat until hot (around 350°F).
Carefully add the breaded apple wedges to the hot oil in batches, frying until golden brown on all sides, about 3-4 minutes. Remove and drain on paper towels.
For the caramel cream dip, in a medium bowl, combine the softened cream cheese, caramel sauce, powdered sugar, and vanilla extract. Mix until smooth and creamy.
Serve the apple fries warm with the caramel cream dip on the side.