Preheat oven to 375 degrees. In a mixing bowl, whisk together flour, baking powder, baking soda, cinnamon, ginger, nutmeg and salt, set aside. In the bowl an electric stand mixer fitted with paddle attachment and set on medium speed, whip together butter, light-brown sugar and granulated sugar until pale and fluffy, about 3 - 4 minutes.
Add in eggs one at a time, mixing after each addition until combine. Mix in sour cream and vanilla extract, then mix in pumpkin puree. With mixer set on low speed, slowly add dry ingredients and mix until combine (be sure to scrape down bowl throughout entire mixing process).
Transfer 1 1/2 cups of the cookie dough to a pastry bag fitted with a 1/2-inch plain tip and pipe 1 1/2-inch rounds onto a Silpat or parchment paper lined cookie sheets, spacing cookies at least 1 inch apart*. Bake in preheated oven about 12 minutes until tops spring back when touched. Allow to cool several minutes on baking sheet before transferring to a wire rack. Cool completely then prepare icing and spread icing over cookies. Store in an airtight container in a single layer in refrigerator and rest at room temperature before serving.
*Alternately you can drop dough by the tablespoonfuls onto the lined baking sheets (they just won't look as nicely circular). You can make them larger than listed in the recipe (which is what I did after the first batch because the 1 1/2-inch rounds yields pretty small cookies). If you do decide to pipe them bigger just allow a little more space between each cookie.
Browned Butter Icing
Measure 4 cups of powdered sugar into a mixing bowl, set aside. Brown butter in a small saucepan over medium heat, swirling pan occasionally (butter will melt, after a few minutes it will splatter, then it will foam, then golden brown flecks will begin to appear in the center of the foamy bubbles. This is when you remove it from heat - I wait for for the flecks to expand to about a 1 1/2 to 2-inch circle over the foam then immediately remove).
Carefully pour browned butter over powdered sugar in mixing bowl, use a rubber spatula to scrape any excess butter and browned bits from pan. Add half and half and stir mixture until smooth. Spread over cookies, adding additional half and half, about 1 - 2 tsp at a time, to icing mixture to thin as it will thicken as it sits.