Core and peel apples, then cut into small cubes. In small saucepan on medium-low heat, saute butter until melted, then add apples, sugar, cinnamon, and 1 teaspoon water and stir to coat. Cook until apples have softened slightly, stirring often (about 5 minutes). Apples will cook down a little and sauce will be similar to syrup. Remove from heat to cool.

Carefully unfold pie crusts onto parchment paper. Use a rolling pin to roll out smooth and even. To make circles, place bowl upside down and trace around with sharp knife. Remove circles, then roll out extra dough to make additional circles. (Bowl used was 4 inches in diameter) You should be able to get 12 circles out total.

Place about 1 tablespoon of apples into the center of each dough circle. Fold in half and press seam slightly with fingers. Using a fork, press to meld seams together. Prepare egg wash in small bowl by whisking egg and 1 teaspoon water. Slit dough with sharp knife. (optional) Brush both sides of each pie with egg wash.

Spray or grease air fryer basket with butter. Place pies into basket leaving room in between. Cook on 350 degrees for 5 minutes, then flip and cook another 5 minutes. Pies should be golden brown. Remove from air fryer and serve with warm caramel sauce.