Preheat a pizzelle maker with 4 ½-inch molds or a waffle cone maker.
Melt the butter in a small saucepan and allow it to cool slightly.
In a medium-sized bowl, whisk together the whole egg, egg white, sugar,vanilla and melted butter until smooth. Add the flours, cocoa and salt and whisk until smooth again. Let the batter rest for about 5 minutes.
Scoop 1 tablespoon of the batter onto the center of the pizzelle maker. Close the lid and cook for 30–60 seconds or until the cookie is done.