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

In a mixing bowl, combine the flour, baking soda, baking powder, cinnamon, nutmeg, and salt. Stir until well-blended.

In another bowl, use an electric mixer to cream together the softened butter, granulated sugar, and brown sugar until light and fluffy, about 2-3 minutes.

Beat in the egg and vanilla extract, mixing until fully combined.

Next, mix in the pumpkin puree until the mixture is smooth.

Gradually add the dry ingredient mixture to the pumpkin mixture, stirring until just combined. Do not overmix.

In a separate bowl, beat together the softened cream cheese and powdered sugar until smooth and creamy.

Using a cookie scoop or tablespoon, drop dollops of the pumpkin cookie dough onto the prepared baking sheet, leaving some space between each cookie.

Using a small spoon or your fingers, make an indentation in the center of each cookie and fill it with a dollop of the cream cheese mixture.

Bake in the preheated oven for 10-12 minutes, or until the edges are lightly golden.

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