Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper to prevent sticking.

In a medium bowl, whisk together the flour, baking soda, baking powder, cinnamon, nutmeg, ginger, and salt. This helps to evenly distribute the leavening agents and spices.

In a large mixing bowl, cream together the softened butter, granulated sugar, and brown sugar using an electric mixer on medium speed until light and fluffy, about 3-4 minutes.

Add the pumpkin puree, egg, and vanilla extract to the butter mixture. Mix until well combined.

Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Be careful not to overmix, as this can make the cookies tough.

Using a cookie scoop, drop tablespoon-sized balls of dough onto the prepared baking sheet, spacing them about 2 inches apart.

Bake in the preheated oven for 12-15 minutes, or until the edges are set and the tops are slightly cracked. The cookies will continue to firm up as they cool.

Remove from the oven and let the cookies cool on the baking sheet for 5 minutes before transferring them to a cooling rack to cool completely.

In a large mixing bowl, beat the softened cream cheese and butter together with an electric mixer on medium speed until smooth and creamy, about 2-3 minutes.

Gradually add the sifted powdered sugar, mixing on low speed until incorporated. Increase the speed to medium and beat until fluffy.

Add the vanilla extract and mix until combined. If the frosting is too thick, add milk one tablespoon at a time until you reach your desired consistency.

Once the cookies are completely cool, spread a generous amount of cream cheese frosting on top of each cookie using a spatula or a piping bag.