In the bowl of an electric stand mixer fitted with the paddle attachment whip together butter, granulated sugar and brown sugar until pale and fluffy. Scrape down bowl.
Mix in egg and vanilla. With mixer set on low speed, slowly mix in half of the flour mixture, then mix in the zucchini and finish by mixing in remaining flour mixture.
Drop batter into balls, 2 Tbsp (even) at a time, onto parchment paper or Silpat lined baking sheets, spacing cookies 2-inches apart.
Bake in preheated oven 10 - 13 minutes (careful not to over-bake, they should still be soft to the touch. They will continue to cook for about a minute when removed from the oven).
Cool on baking sheet 2 minutes, then transfer to a wire rack to cool completely. Once cool, frost cookies with cream cheese frosting and sprinkles tops very lightly with cinnamon and nutmeg if desired.
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