To Make the Cookies:
Preheat your oven to 350°F (175°C). Line two baking sheets with parchment paper or silicone baking mats.
In a large mixing bowl, using an electric mixer, beat together the softened butter and granulated sugar until the mixture is light and creamy, about 2-3 minutes.
Add the pumpkin puree, egg, and vanilla extract to the butter mixture. Beat on low speed until well combined.
In a separate bowl, whisk together the all-purpose flour, baking powder, cinnamon, salt, ginger, and nutmeg.
Gradually add the dry ingredients to the wet mixture in a few additions, mixing on low speed after each addition until fully combined. Be sure to scrape down the sides and bottom of the bowl to ensure everything is mixed evenly.
Cover the dough with plastic wrap and refrigerate for 30 minutes to make it easier to handle.
To Roll and Bake:
While the dough is chilling, prepare the cinnamon-sugar mixture for rolling. In a small bowl, combine the granulated sugar and cinnamon. Set aside.
Once the dough has chilled, scoop about 2 tablespoons of dough and roll it into a ball. Then, roll the ball in the cinnamon-sugar mixture to coat it evenly.
Place the coated dough balls onto the prepared baking sheets, spacing them about 1 inch apart. Gently press down on each dough ball with a spoon or your palm to slightly flatten them.
Bake the cookies in the preheated oven for 10-12 minutes, or until the edges are just beginning to brown slightly.
Remove the cookies from the oven and allow them to cool completely on the baking sheets.
To Make the Cream Cheese Frosting:
In a mixing bowl, beat together the softened cream cheese, butter, vanilla extract, and salt until smooth and creamy.
Gradually add the powdered sugar, beating on low speed until fully incorporated. Once all the sugar is added, increase the speed to medium and beat until the frosting is smooth and fluffy.
To Frost the Cookies:
Once the cookies have cooled completely, spread a generous amount of cream cheese frosting on top of each cookie.
For an extra touch, sprinkle the frosted cookies with a little additional cinnamon.
Serve and enjoy!
Storage: Store any leftover cookies in an airtight container in the refrigerator for up to 5 days.