1. Position a rack in the center of the oven and preheat to 340˚F.
2. Cream the sugar and butter together in the bowl of a stand mixer fitted with the paddle attachment, starting on low speed and gradually increasing to medium. (You can use a hand mixer if you let the butter soften at room temperature before beginning.) Add the eggs, one at a time, paddling about 1 minute after each egg is added, then stopping after each one to scrape the sides. Add the milk, vanilla, and lemon juice and paddle just until they are absorbed into the mixture.
3. Sift the cake flour, all-purpose flour, baking powder, and salt together into a separate bowl. Add them to the mixer bowl. Paddle on low speed just until they have been absorbed by the mixture and it is smooth and consistent.
4. Line two cookie sheets with parchment paper, using nonstick spray or a dab of butter in each corner to glue the paper in place.
5. Use a 2-ounce ice cream scoop to portion the batter onto the parchment paper, leaving 2 inches between the cookies.
6. Bake in batches until the cookies are light golden, about 18 minutes. Remove the cookie sheets from the oven. As soon as the cookies can be moved, use a spatula to transfer them to a rack and let them cool.
7. Transfer the cookies to plates and place in a freezer for about 20 minutes to firm them up.
8. Meanwhile, bring the water to a boil in the top of a double-boiler set over simmering water. Whisk in the 10X sugar until the mixture is uniformly smooth and white. Use a spatula to ice half of the top of each cookie, using the edge of the spatula or the tip of a thin-bladed knife to make a straight edge. (If the icing seizes up, simply return the pot to the double-boiler over low heat and whisk to reinvigorate.)
9. Return the pot to the double boiler and stir the chocolate into the remaining icing until it melts and is blended in. Spread the chocolate frosting over the other half of each cookie. Serve immediately, or store in an airtight container at room temperature for up to 3 days.
Excerpt from "Baking with the Cake Boss" by Buddy Valastro. Copyright © 2011 by Buddy Valastro. Used with permission by Atria Books. All rights reserved.