Blot Pumpkin & Prep: Spread pumpkin puree between paper towels to absorb excess moisture. Preheat oven to 350°F (175°C) and line two baking sheets with parchment paper.
Cream Butter & Sugars: In a stand mixer fitted with paddle, beat softened butter, brown sugar, and granulated sugar on medium-high speed for 2-3 minutes until light and fluffy. Beat in pumpkin puree, egg, and vanilla until smooth.
Combine Batter: Whisk flour, baking powder, baking soda, salt, cinnamon, and pumpkin pie spice in a bowl. Gently fold into the wet mixture just until incorporated.
Scoop & Bake: Drop 2-tablespoon mounds of dough onto prepared sheets. Bake at 350°F for 12-14 minutes until tops spring back lightly. Cool completely on wire rack.
Glaze & Set: Whisk powdered sugar, maple syrup, milk, and extra vanilla until smooth. Spoon over cooled cookies and let set for 15 minutes before serving.