Preheat oven to 350 degrees. Line cupcake pans with paper liners; set aside. In a medium bowl, whisk together flour, baking soda, baking powder, salt, cinnamon, ginger, nutmeg, and allspice; set aside.
In a large bowl, whisk together, brown sugar, granulated sugar, butter, and eggs. Add dry ingredients, and whisk until smooth. Whisk in pumpkin puree.
Divide batter evenly among liners, filling each about halfway. Bake until tops spring back when touched, and a cake tester inserted in the center comes out clean, 20 to 25 minutes, rotating pans once if needed. Transfer to a wire rack; let cool completely.