Preheat your oven to 350°F (175°C) and line two baking sheets with parchment paper.

In a large mixing bowl, cream together the softened butter, granulated sugar, and brown sugar with an electric mixer until light and fluffy, about 2-3 minutes. Scrape down the sides of the bowl as needed.

Add the pumpkin puree, egg, and vanilla extract to the creamed mixture. Beat until just combined; do not overmix at this stage.

In a separate bowl, whisk together the flour, baking soda, baking powder, salt, and pumpkin pie spice.

Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Stop mixing as soon as no dry streaks remain to avoid tough cookies.

Use a cookie scoop (about 1.5-inch diameter) to drop mounds of dough onto the prepared baking sheets, spacing them about 2-3 inches apart.

Bake for 10-12 minutes, or until the edges are lightly golden and the centers are set but still soft. Overbaking will make them dry.

Let the cookies cool on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely. They need to be fully cool before glazing.

In a small saucepan, melt 2 tablespoons of butter over medium heat. Stir in the pure maple syrup and powdered sugar until smooth.

Cook, stirring constantly, for about 1-2 minutes until the glaze thickens slightly. It should be pourable but not watery. Optionally, add a pinch of pumpkin pie spice for extra flavor here.

Remove from heat and, if needed, whisk in milk one teaspoon at a time until you reach your desired drizzling consistency. It should be thick enough to cling to the cookies.

Once the cookies are completely cool, drizzle or spread the maple glaze over each one. Let the glaze set for about 30 minutes before stacking or storing.