Pizzelle (Italian Christmas Cookies)

In a large bowl or the bowl of a stand mixer, beat together the eggs, sugar, salt, and vanilla until well combined., Stir in the flour and baking powder, mixing until smooth., Add the melted butter, again mixing until smooth; the batter will be thick and soft., Heat your pizzelle iron. Grease it as directed in the manufacturer's instructions. As the iron heats, the batter will stiffen., Cook the pizzelle according to the instructions that came with your iron. In general, they'll take between 45 seconds and 2 1/2 minutes to brown., Remove the pizzelle from the iron, and cool on a rack. If desired, use a pair of scissors to trim any ragged edges., Dust cooled pizzelle with confectioners' sugar, if desired., Pizelle are best eaten immediately, but leftovers can be stored for up to 1 week in an airtight container, or frozen for up to a 1 month.