Pumpkin Cookies with Brown Butter Icing

In a large mixing bowl, cream together the softened butter, white sugar, and brown sugar until smooth. Add the pumpkin puree, egg, and vanilla. Beat until well-blended. In another bowl, whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, cloves, and pumpkin pie spice. Gradually add the dry ingredients to the pumpkin mixture, beating until just combined. Drop tablespoonfuls of dough onto cookie sheets and flatten slightly with a spoon. Bake at 350°F (175°C) for 10-12 minutes, or until the edges are lightly browned. Remove from oven and transfer cookies to a wire rack to cool completely. Place powdered sugar in a medium bowl and set aside. Melt the unsalted butter in a small saucepan over low-medium heat, stirring frequently. Cook until the butter foams, the foam dissipates, and it turns a deep golden brown with a nutty aroma, about 10 minutes. Be attentive to avoid burning. Remove from heat and let cool for 2-3 minutes. Carefully pour the brown butter over the powdered sugar. Add milk and vanilla , then vigorously whisk the mixture until smooth. If the icing seems to seize or separate, continue whisking until fully emulsified and smooth. An electric mixer can be used if preferred. The icing should be thin enough to spread easily but not too runny. Adjust consistency with more milk or powdered sugar if needed. Spread approximately 1 tablespoon of icing