Preheat oven to 350°F (175°C). Line two baking sheets with parchment paper or silicone baking mats.
In a medium bowl, whisk together flour, baking powder, baking soda, cinnamon, nutmeg, ginger, cloves, and salt. Set aside.
In a large mixing bowl, cream butter, granulated sugar, and brown sugar until light and fluffy, about 2–3 minutes.
Beat in egg and vanilla extract until combined. Mix in pumpkin puree and maple syrup until smooth.
Gradually add dry ingredients to wet mixture, mixing on low until just combined.
Scoop tablespoons of dough onto prepared sheets, spacing 2 inches apart. Bake 12–15 minutes, until edges are set and tops are slightly puffed.
Cool cookies on sheet for 5 minutes, then transfer to wire rack to cool completely.
In a small bowl, whisk powdered sugar, maple syrup, milk or cream, and vanilla until smooth. Adjust consistency as needed.
Once cookies are fully cool, drizzle or spread glaze on top. Let set for 10 minutes before serving.