In a large mixing bowl, cream together the softened butter and brown sugar using a hand mixer or stand mixer. Add pumpkin puree and vanilla extract, and mix well until smooth.

In a separate bowl, whisk together flour, baking powder, baking soda, cinnamon, nutmeg, and salt.

Gradually add the dry ingredients to the pumpkin mixture, stirring gently until well combined.

Cover the dough and refrigerate overnight or for at least 8 hours.

Preheat your oven to 350°F (175°C). Line a cookie sheet with parchment paper.

Scoop 1-tablespoon-sized portions of dough onto the cookie sheet, spacing them about 2 inches apart. Flatten each cookie slightly with the back of a spoon to about 1/4-inch thickness.

Bake for 12-15 minutes, or until the cookie bottoms start to lightly stick to the parchment paper.

Allow the cookies to cool for 5-10 minutes on the sheet before transferring them to a cooling rack.

For the icing, whisk together powdered sugar, maple syrup, and half-and-half in a small bowl until smooth.

Drizzle the icing over the cooled cookies using a spoon. Allow the icing to harden for about 1 hour before serving or storing.