Preheat an oven to 350 degrees F (175 degrees C). Whisk together the flour, baking powder, baking soda, and salt in a bowl; set aside. Grease 2 baking sheets
Beat the butter and sugar with an electric mixer in a large bowl until fluffy. Beat in one egg until completely incorporated, then another. Beat in the last egg along with the anise extract. Mix in the flour until just incorporated.
This batter will be wet and sticky! Using a rubber spatula, divide the dough onto the prepared baking sheets. Form each portion into a 12"-inch long log, 1"-inch thick.
Bake in the preheated oven until golden and firm to the touch, 20 to 25 minutes. Remove from the oven, and allow to cool 5 minutes. Cut into 3/4-inch thick slices using a serrated knife, and place cut-side-down onto the baking sheets. Return to the oven, and bake 5 to 10 minutes until the bottoms turn light golden brown. Turn the cookies over, and continue baking until light golden brown on the other side, 5 to 10 minutes more. Cool completely on a wire rack before serving.