Preheat oven to 350°F. Line a baking sheet with parchment paper or a silicone baking mat.

In a large bowl, combine flour, baking powder, baking soda, homemade pumpkin pie spice, and salt; set aside.

In the bowl of a stand mixer fitted with the paddle attachment, or in a large bowl with an electric mixer, cream together the butter and sugars. Add pumpkin, egg, and vanilla to the butter mixture. Beat on medium speed until fully incorporated and creamy. Slowly add in dry ingredients and mix until combined. Using a medium cookie scoop (1 1/2 tablespoons), drop dough onto prepared cookie sheets. Spray the bottom of a glass with nonstick cooking spray and ever so slightly, flatten the tops of the cookies.

Bake in the preheated oven for 12-15 minutes. Allow cookies to cool on the pan for a few minutes before removing them to a wire rack to cool completely.

To Make the Glaze: Combine confectioners' sugar, milk, melted butter, and vanilla. Add milk as needed, to achieve glaze consistency.

Place a piece of parchment or wax paper on your work surface and place a wire rack on top of the paper. Dip the top of each cookie into the glaze and place the cookie onto the wire rack allowing the glaze to drizzle down the sides of the cookie. Allow glaze to firm up before serving.