Preheat your oven to 350°F (175°C). Line your baking sheets with parchment paper or silicone baking mats to prevent sticking and allow for easy cleanup.
In a medium bowl, whisk together the all-purpose flour, baking soda, baking powder, cinnamon, nutmeg, ginger, and salt. Set aside.
In a large bowl, use an electric mixer to cream the softened butter and granulated sugar until light and fluffy, about 2-3 minutes.
Beat in the pumpkin puree, vanilla extract, and egg until fully combined. The mixture will look smooth and creamy.
Gradually add the dry ingredients to the wet ingredients, mixing on low speed just until combined. Be careful not to overmix.
Using a cookie scoop or tablespoon, drop dough onto the prepared baking sheets, spacing them about 2 inches apart. Bake for 12-14 minutes or until edges are set and bottoms are lightly golden.
Transfer the cookies to a cooling rack and let them cool completely before frosting.
In a bowl, beat the softened cream cheese until smooth. Gradually add powdered sugar and vanilla extract, mixing until light and fluffy.
Once the cookies are cooled, spread a generous layer of cream cheese frosting on each one using an offset spatula or butter knife.
Serve these Pumpkin Sugar Cookies with Cream Cheese Frosting immediately or chill them for a firmer frosting texture.