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Preheat oven to 350 degrees and line baking sheet with parchment paper.
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In a small bowl, whisk together flour, baking powder, salt and pumpkin pie spice.
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In the bowl of a stand mixer, combine sugar and butter, and beat with paddle attachment until fluffy.
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Add egg and vanilla, and continue beating until combined.
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Add flour mixture and stir just until combined.
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Scrape down sides of bowl as needed.
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Roll two tablespoons of cookie dough into a ball and place on baking sheet.
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Bake for about 10 minutes, or until edges are golden. Don't over bake.
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Let cool and frost.
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Sprinkle cookies with additional pumpkin pie spice.
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To prepare frosting, using the paddle attachment, beat butter, powdered sugar, pumpkin pie spice, and pinch of salt in the bowl of a stand mixer.
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With mixer still running, add in vanilla extract.
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Divide cream cheese into 8 cubes and drop them into the mixture one at a time until well combined.