In a medium bowl, whisk together the sifted flour, baking soda, baking powder, salt, and pumpkin pie spice. Set aside.

In a large bowl, using an electric mixer, cream together the softened butter, granulated sugar, and light brown sugar on medium speed until light and fluffy, about 2-3 minutes.

Beat in the pumpkin puree, egg, and vanilla extract until well combined and smooth, scraping down the sides of the bowl as needed.

Gradually add the dry ingredient mixture to the wet ingredients, mixing on low speed until just combined. Do not overmix. The dough will be soft.

Cover the bowl with plastic wrap and chill the dough in the refrigerator for at least 15-20 minutes. This helps prevent spreading.

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

Using a 1.5-inch cookie scoop or two spoons, drop rounded spoonfuls of dough onto the prepared baking sheets, about 2 inches apart.

Bake for 10-13 minutes, or until the edges are set and lightly golden, and the centers are still slightly soft. They will puff up slightly. Baking time may vary depending on your oven.

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

While the cookies are cooling, prepare the glaze. In a medium bowl, beat the softened cream cheese and butter with an electric mixer until smooth and creamy.

Add the sifted powdered sugar, 1 tablespoon of milk, vanilla extract, and a pinch of salt. Beat on low speed until combined, then increase to medium and beat until smooth. If the glaze is too thick, add the remaining milk 1 teaspoon at a time until desired consistency is reached.

Once the cookies are completely cool, drizzle or spread the cream cheese glaze generously over each cookie. Allow the glaze to set for about 15-20 minutes before serving.