Preheat the oven to 350°F (180°C). Line a baking sheet with parchment paper to prevent sticking.
In a large bowl, combine softened butter, granulated sugar, and brown sugar. Use an electric mixer to beat until the mixture becomes fluffy and creamy, which takes about 5 minutes. Add the egg yolk, pumpkin puree, and vanilla extract, then mix again until everything is well 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. Gradually add the dry ingredients to the wet mixture, stirring just until combined. Avoid overmixing to maintain a soft cookie texture.
1 ⅔ cups flour, 1 tablespoon pumpkin spice, 1 teaspoon baking powder, ¼ teaspoon salt
Scoop 2-tablespoon-sized balls of dough onto the prepared baking sheet. Gently flatten each ball with your hands. Bake in the preheated oven for 10 minutes. Let the cookies cool completely on a wire rack before frosting.
To prepare the frosting, beat the softened cream cheese, butter, and caramel sauce together in a bowl until smooth. Gradually add the powdered sugar, mixing until the frosting is thick and creamy. Transfer the frosting to a piping bag.
½ cup cream cheese, 4 tablespoons butter, 4 tablespoons caramel sauce, ¾ cup powdered sugar
Once the cookies are completely cool, pipe a thick swirl of frosting onto each one. Lightly sprinkle with cinnamon powder to finish.