Sift flour, baking powder, cinnamon, baking soda, nutmeg, allspice, ginger, and salt into a bowl.
Beat butter, white sugar, and brown sugar in a bowl until smooth and creamy. Mix in honey, egg, and lemon zest until well blended. Fold in sweet potato. Stir in flour mixture with a large spoon until dough is just blended.
Shape tablespoonfuls of dough into balls and place 2 inches apart on ungreased baking sheets.
Bake in the preheated oven until edges start to brown, about 8 minutes. Cool on the baking sheets for 5 minutes; transfer to wire racks to cool completely, about 10 minutes.