Preheat oven to 350°F (175°C). Line a baking sheet with parchment paper.
In a large bowl (or the bowl of your stand mixer), cream together 1 cup (2 sticks) of softened unsalted butter, 1 cup of granulated sugar, and 1/2 cup of packed light brown sugar. Beat on medium speed until light and fluffy, about 3-4 minutes.
Beat in 1 cup of pumpkin puree (make sure it's pumpkin puree, NOT pumpkin pie filling!) and 1 teaspoon of pure vanilla extract. Mix until just combined.
In a separate bowl, whisk together 2 1/2 cups of all-purpose flour, 1 teaspoon of baking soda, 1 teaspoon of baking powder, 1 teaspoon of ground cinnamon, 1/2 teaspoon of ground ginger, 1/4 teaspoon of ground cloves, and 1/4 teaspoon of salt.
Slowly add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Avoid overmixing.
Wrap the dough tightly in plastic wrap and chill in the refrigerator for at least 30 minutes, or up to 2 hours.
Use a large cookie scoop (about 1/4 cup) to drop rounded mounds of dough onto the prepared baking sheet, leaving about 2 inches between each cookie.
Bake for 12-15 minutes, or until the edges are set and the centers are slightly soft. Don't overbake!
Let the cookies cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.
In a large bowl (or the bowl of your stand mixer), beat 8 ounces of softened cream cheese and 1/2 cup (1 stick) of softened unsalted butter until smooth and creamy. Make sure your cream cheese and butter are at room temperature for the best results.
Gradually add 4 cups of powdered sugar, beating on low speed until combined.
Beat in 1 teaspoon of pure vanilla extract.
If the frosting is too thick, add a tablespoon of milk or cream at a time until you reach your desired consistency. If it's too thin, add more powdered sugar, a tablespoon at a time.
Once the cookies are completely cool, generously frost the tops with the cream cheese frosting. You can use a knife, spatula, or piping bag for this step.
For that authentic pumpkin pie look, use a fork to create swirl patterns on the frosting (optional).
Sprinkle with a pinch of ground cinnamon, a drizzle of caramel sauce, or a sprinkle of chopped pecans for extra flair (optional).
Chill the assembled cookies for at least 30 minutes before serving. This allows the frosting to set and the flavors to meld together even more.