Cook diced apple with butter, brown sugar, cinnamon, and nutmeg over medium heat 3 to 4 minutes. Stir in cornstarch and water mixture, cook 1 minute until thickened. Add vanilla and cool 5 minutes.
Warm tortillas until pliable. Mix cinnamon sugar coating in a shallow bowl.
Fill each tortilla with 2 tbsp apple filling in a tight line. Roll firmly and place seam-side down.
Brush each taquito with melted butter on all sides. Roll in cinnamon sugar to coat evenly.
Preheat air fryer to 375°F. Air fry seam-side down in a single layer 6 to 8 minutes, flipping halfway, until deep golden. Serve immediately.