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Preheat oven to 350 degrees and line a baking sheet with parchment paper.
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In a bowl, cream butter, brown sugar, and granulated sugar together until well combined.
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Add in the egg, and mix until well combined.
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Add in pumpkin puree, mixing until combined.
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Next, add in allspice, nutmeg, cloves, cinnamon, vanilla extract, baking powder, baking soda, and salt. Mix until everything is combined.
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Add in flour and mix until flour is well incorporated.
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With a small-med sized cookie scoop (about 1 1/2 - 2 Tbsp), scoop dough and place evenly on your prepared cookie sheet.
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Bake for about 12-13 minutes, or until cookies are set. Allow to cool completely before frosting.
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With a standing mixer or hand mixer beat butter until light and fluffy, about 1-2 minutes. Add in maple syrup and vanilla extract. Beat until well combined.
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Add in powdered sugar, 1/2 cup at a time, mixing until well combined (beginning with 1 1/2 cups).
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Add in 2 tsp of milk and beat until combined.
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If frosting feels too runny, add in the remaining 1/2 cup of powdered sugar. If it feels too thick, add in the remaining tsp of milk.
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Spread frosting on cookies.
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Enjoy!