In a large bowl, beat eggs and sugar until thick. Stir in the melted butter and vanilla. Sift together the flour, cocoa and baking powder and blend into the batter until smooth.
Heat the pizzelle iron and brush well with oil. Drop about one tablespoon of batter onto each circle on the iron. You may need to experiment with the amount of batter and baking time depending on the iron. Bake for 20 to 45 seconds, or until steam is no longer coming out of the iron. Carefully remove biscuits from the iron. Oil the iron again before beginning the next batch. Cool completely before storing in an airtight container.