Slice the apples: Peel and core the apples, then cut them into wedges about 1/2 inch thick so they cook at the same rate. Pat each wedge dry with a paper towel to help the coating stick.
Season the flour: In a shallow bowl, whisk together the flour, 1 teaspoon cinnamon, and nutmeg. This first layer helps the egg wash cling evenly to the apple.
Set up egg wash: In a second bowl, beat the eggs with the milk until smooth. Place the panko breadcrumbs in a third shallow bowl nearby.
Dredge each wedge: Coat an apple wedge in the seasoned flour, shaking off excess, then dip it into the egg mixture. Press it into the panko, turning to coat all sides and pressing gently so the crumbs adhere.
Preheat the air fryer: Set the air fryer to 375°F and let it run empty for 3 minutes. A hot basket helps the coating start crisping right away instead of steaming.
Arrange in a single layer: Place the coated wedges in the basket without touching, working in batches if needed. Mist the tops lightly with cooking spray.
Cook the first side: Air fry for 6 minutes, until the panko at the edges turns light golden. Open the basket to check color rather than guessing by time alone.
Flip and spray again: Flip each wedge with tongs, spray the other side, and air fry for another 5 to 6 minutes until deep golden brown and crisp all over.
Toss in cinnamon sugar: Mix the granulated sugar with 1 tablespoon cinnamon in a wide bowl. While the apple fries are still warm, toss them gently in the mixture until evenly coated.
Serve with caramel: Arrange the apple fries on a plate with a small bowl of warm caramel sauce for dipping. Serve them right away while the coating is at its crispest.