Whisk together gluten-free baking flour, granulated sugar, and baking powder in a medium bowl. Switch to a wooden spoon and stir in eggs, cooled, melted butter, and anise extract. Batter will be thick and soft.
Heat pizzelle iron according to manufacturer's directions. Grease with nonstick cooking spray. Spoon batter onto hot iron. Bake until lightly golden brown.
Remove hot pizzelles from iron. Transfer to a wire rack to cool. Dust cooled pizzelles with powdered sugar, if desired.