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In a medium bowl, combine flour, baking soda, baking powder, salt, cinnamon, ginger, nutmeg, and allspice; set aside.
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In a large bowl, mix brown sugar, granulated sugar, butter, and eggs. Add dry ingredients, and mix until smooth. Stir in pumpkin puree.
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Divide batter into lined cupcake tins, filling each about halfway. Bake at 350 for 20 to 25 minutes or until test done with toothpick.