Line the air fryer basket with parchment paper.
In a large mixing bowl, combine the softened butter, granulated sugar, and brown sugar. Beat with an electric mixer on medium speed for about 5 minutes, or until light and fluffy. Mix in the egg yolk, pumpkin puree, and vanilla extract until fully combined.
½ cup unsalted butter, ½ cup granulated sugar, ¼ cup brown sugar, 1 egg yolk, ¼ cup pumpkin puree, 1 tablespoon vanilla extract
In a separate bowl, sift together the flour, pumpkin spice, baking powder, and salt into the wet mixture, mixing until a soft dough forms.
1 ⅔ cups all-purpose flour, 1 tablespoon pumpkin spice, 1 teaspoon baking powder, ¼ teaspoon salt
Scoop about 2 tablespoons of dough for each cookie, roll into balls, and gently flatten them with your hands. Arrange them in the prepared air fryer basket, leaving some space between each cookie.
Air fry at 350°F (180°C) for about 6 minutes, or until the edges are set and the tops look slightly golden. Allow the cookies to cool completely before frosting.
In a medium bowl, beat together the cream cheese, butter, caramel sauce, and powdered sugar with an electric mixer until smooth and creamy.
½ cup cream cheese, 4 tablespoons butter, 4 tablespoons caramel sauce, ¾ cup powdered sugar
Transfer the frosting to a piping bag and pipe a thick swirl on top of each cooled cookie. Lightly sprinkle cinnamon powder over the top for extra flavor.