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Whisk together all ingredients except additional butter in a bowl until smooth. Chill batter, covered, 1 hour.
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Heat pizzelle maker and lightly brush top and bottom of pizzelle molds with butter. Pour 1 tablespoon batter into bottom of each pizzelle mold. Close cover and cook batter until golden, about 2 minutes.
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Working quickly (pizzelle are pliable only while hot), peel off 1 pizzella and wrap around cone mold, overlapping ends, and pinching tip closed. Hold cone in place until it hardens, about 5 seconds, then slip off mold and repeat with remaining pizzelle. Make more pizzelle and cones in same manner.