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, beat the softened butter, granulated sugar, and brown sugar together using an electric mixer on medium speed until light and fluffy, about 3-4 minutes. This incorporates air into the mixture, which helps the cookies rise.

Add the pumpkin puree, egg, and vanilla extract to the butter mixture. Beat 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 lead to tough cookies.

Using a cookie scoop or tablespoon, drop rounded 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 medium bowl, beat the softened cream cheese and butter together with an electric mixer on medium speed until smooth and creamy.

Gradually add the sifted powdered sugar, mixing on low speed until combined. Increase the speed to medium and beat until fluffy, about 2-3 minutes.

Add the vanilla extract and mix until well incorporated.

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 for a decorative touch.

Serve immediately or store in an airtight container in the refrigerator for up to 5 days.