Adjust rack to lower third of oven and preheat oven to 350 degrees F. Line a cookie sheet with baking parchment.
In a bowl, combine the flour, baking powder, cinnamon, nutmeg, cloves, and salt with a rubber spatula; set aside. In a separate bowl, using an electric mixer, beat butter and sugar until just light. Lower speed and mix in egg. Stir in flour mixture until well blended. Stir in zucchini.
Drop tablespoonfuls of batter onto the baking sheet. Bake for 12 to 14 minutes, or until golden brown.