Preheat oven to 350°.
Beat butter with an electric mixer on high speed for 30 seconds, scraping sides if needed. Add sugar, salt, baking powder, baking soda, and pumpkin pie spice. Beat until combined, scraping the sides of the bowl. Add eggs and vanilla, beating until combined. Beat in pumpkin. Mix in flour until combined.
Drop dough, using a 2 tablespoon medium scoop onto a parchment lined baking sheet. Bake for 9-11 minutes in preheated oven until tops are set. Allow cookies to cool before frosting.
Whip butter and cream cheese together in mixer. Alternate adding powdered sugar and milk until well combined and nice and creamy. Add vanilla.
Spread frosting on each cookie and sprinkle with a little pinch of pumpkin pie spice.