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

In a large bowl, cream together the softened butter, granulated sugar, and brown sugar until light and fluffy.

Add the pumpkin puree, eggs, and vanilla extract to the mixture. Mix well until everything is combined.

In a separate bowl, whisk together the flour, baking soda, baking powder, cinnamon, nutmeg, ginger, and salt.

Gradually incorporate the dry ingredients into the wet mixture until just combined, avoiding overmixing.

Drop rounded tablespoons of dough onto the prepared baking sheet, spacing them about 2 inches apart.

Bake for 12-15 minutes or until the edges are lightly golden; the centers may appear soft.

Allow cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.

In a medium bowl, beat the softened cream cheese until smooth.

Gradually add the powdered sugar, continuing to mix until combined.

Add the milk and the additional vanilla extract as needed to achieve your desired consistency.

Once the cookies are completely cool, spread a generous layer of cream cheese frosting on top of each cookie.