In large bowl, with electric mixer at medium speed, beat eggs until very thick and light. Gradually beat in sugar. Continue beating 20 minutes longer. At low speed, beat in flour, baking powder, salt; beat 1 minute. Add anise extract; beat just until blended.
Drop by teaspoonfuls, 1/2 inch apart, on prepared cookie sheets. Swirl each, to make into a circle. Let stand at room temperature, uncovered, 8 hours, or overnight.
Preheat oven to 325 degrees F.
Bake cookies about 10 minutes, or until smooth and firm when pressed with fingertip. Cool cookies on wire rack. Then store in airtight container.