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Preheat oven to 350 degrees. Line 12 cupcake cups with paper liners; set aside. In a medium bowl, whisk together flour, baking soda, baking powder, salt, cinnamon, ginger, nutmeg, and allspice; set aside.
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In a large bowl, whisk together, brown sugar, granulated sugar, butter, and eggs. Add dry ingredients, and whisk until smooth. Whisk in pumpkin puree.
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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. Transfer to a wire rack; let cool completely.