In a medium-sized mixing bowl, whisk the eggs and granulated sugar together until pale and slightly fluffy, about 1-2 minutes. Gently whisk in the melted and cooled butter and the anise extract until just combined.

In a separate bowl, stir together the all-purpose flour, baking powder, and salt. Gradually add the dry ingredients to the wet ingredients, mixing until a smooth, thick batter forms. Do not overmix.

Cover the bowl and let the batter rest in the refrigerator for at least 30 minutes. This step is crucial for achieving an extra-crispy texture.

Preheat your pizzelle iron. Drop about one tablespoon of batter onto the center of each pattern. Close the lid and cook for 45-60 seconds, or until light golden brown. Carefully remove the cookie and transfer it to a wire rack to cool completely. Repeat with the remaining batter.