Preheat oven to 350 degrees. Sift together flours, baking powder, and salt; set aside. In a medium bowl, whisk eggs and sugar until smooth. Add milk, and whisk to combine. Whisk in melted butter and extracts. Add flour mixture, and stir to form a smooth dough. Cover, and chill for 1 hour.
Line baking pans with Silpat nonstick baking mats. Using a 2-ounce scoop, drop five cookies per pan, 3 inches apart. Bake until edges are light brown, 12 to 15 minutes. Transfer cookies to a wire rack set over parchment paper to cool.
In a small bowl, combine confectioners' sugar, 3 tablespoons hot water, and corn syrup. Whisk until smooth. Using a small offset spatula, ice half of each cookie. Return cookies to rack to drip, if necessary.
Add chocolate to remaining icing. Stir until smooth. Add additional corn syrup to thin to desired consistency, if necessary. Spread chocolate icing over second half of each cookie. Allow cookies to set, about 10 minutes.