In a large mixing bowl, whisk together the eggs and granulated sugar until well combined and slightly pale. Gradually whisk in the melted and slightly cooled butter and the anise extract (or chosen flavoring).

In a separate medium bowl, whisk together the all-purpose flour, baking powder, and salt.

Gradually add the dry ingredients to the wet ingredients, mixing until just combined and a smooth, thick batter forms. Be careful not to overmix. The batter should be thick enough to hold its shape on a spoon.

Preheat your pizzelle iron according to the manufacturer's instructions. Most irons will have a light indicator when ready. Lightly grease the iron plates with a neutral oil or non-stick spray, if recommended by your iron's instructions (often only for the first use).

Drop about 1 tablespoon of batter onto the center of each grid design on the preheated pizzelle iron. Close the lid and cook for 30-60 seconds, or until the pizzelle are golden brown and crisp. Cooking time will vary by iron.

Carefully remove the cooked pizzelle with a thin spatula and transfer them to a wire cooling rack to cool completely. They will crisp up further as they cool.

Continue cooking the remaining batter, ensuring to clean any residual batter from the iron between batches if necessary.

Once cooled, dust the pizzelle with powdered sugar if desired.