Whisk together your eggs, sugar, vanilla and anise in a medium bowl. Now add your flour, salt and baking powder and mix it well until there are no lumps and it looks smooth. Now add your melted butter and mix that in to your mixture.
Pre-heat your pizzelle maker. They are all a little different so follow the manufacturers instructions for this. Once it is heated, add a heaping teaspoon of your thick dough to the middle of each of your pizzelle areas on the iron. Close and cook for about 30-45 seconds until it is a light golden color. Once they are cooked, remove the pizzelles from the iron (they will still be soft and pliable at this point) and place on a cooling rack where they will cool and get nice and crispy. Keep doing this until all the dough is used up!
Once all of your pizzelles are fully cooked and cooled, you can go ahead and clean them up if you would like by lightly breaking off any parts of the pizzelle that went beyond the design edge. I find this to be relaxing but it is not necessary :)