Heat a nonstick pizzelle iron. In a small skillet, toast anise seeds over high heat, stirring, until fragrant, about 1 minute. Transfer seeds to a spice grinder, let cool, and finely grind. Scrape into a medium bowl; whisk together with flour, baking powder, and salt.

In a large bowl, whisk together eggs and granulated sugar until well combined. Whisk in vanilla and anise extracts. Slowly add cooled butter in a steady stream, whisking continuously, until batter is smooth. Stir in flour mixture until just combined (do not overmix).

Transfer batter to a piping bag fitted with a 1/2-inch round tip. Pipe about 2 tablespoons batter in a circle around the center of each pattern on the heated pizzelle iron. Close and seal with clasp. Cook until golden brown, about 45 seconds. Using a small spatula, release and remove cookie. Using kitchen shears or a 4 1/2-inch ring mold, trim any ragged edges, if desired. Transfer cookie to a wire rack to cool. Repeat with remaining batter. Dust cooled cookies with confectioners' sugar, if desired.