In a skillet over medium heat, melt the butter. Add the chopped apple, brown sugar, and cinnamon. Cook for 5–7 minutes, stirring occasionally, until apples are soft.
Spoon the apple filling onto one side of each tortilla and roll tightly into taquito shapes.
Brush each taquito with melted butter and roll in cinnamon sugar to coat.
Place taquitos in the air fryer basket in a single layer. Cook at 375°F (190°C) for 5–6 minutes until golden and crispy.
Serve warm with caramel sauce or whipped cream if desired.