In a large mixing bowl, beat the eggs and sugar together until light and fluffy, about 3 minutes.

Add the cooled melted butter and vanilla extract to the egg mixture, and continue to beat until well combined.

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

Gradually fold the dry ingredients into the wet ingredients until the batter is smooth.

Preheat your pizzelle iron according to the manufacturer's instructions.

Place about 1 tablespoon of batter onto each circle of the preheated pizzelle iron. Close the lid and cook for about 30-60 seconds, or until the pizzelle are golden and crisp.

Carefully remove the pizzelle from the iron with a spatula and transfer them to a wire rack to cool.

If desired, dust the cooled pizzelle with powdered sugar before serving.