Preheat your oven to 350ºF (180ºC) and line two baking sheets with parchment paper. In a medium bowl, whisk together the all-purpose flour, baking soda, baking powder, pumpkin pie spice blend, and salt to combine. Set aside.
In a large bowl, use an electric hand mixer or stand mixer to cream together the softened butter and granulated sugar until the mixture is light and fluffy, about 3 minutes. Add the pumpkin puree, cream cheese, and vanilla extract. Beat well, scraping down the sides and bottom of the bowl as needed, until everything is well incorporated.
Add the dry ingredients from Step 1 to the bowl with the creamed mixture from Step 2. Mix on low speed just until combined; do not overmix. You should have a soft dough.
Drop tablespoonfuls of dough onto the prepared baking sheets, spacing them about 2 inches apart. Flatten the mounds slightly with your fingers. For more even cookies, I like to use a small spring-loaded ice cream scoop. Bake in the preheated oven for 15 to 18 minutes until the edges are just starting to brown (the centers will remain soft). Let the cookies cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.
While the cookies cool, combine the powdered sugar, milk, and vanilla extract in a small bowl. Whisk until smooth and pourable. If the glaze is too thick, add a bit more milk, a teaspoon at a time, until you reach the desired consistency.
Once the cookies are completely cooled, drizzle the vanilla glaze from Step 5 over the tops. Allow the glaze to set before serving. I like to add a second layer of glaze for extra sweetness.