I adore these classic cookies for their amusingly large size and cake-like texture. While traditional black and whites are usually frosted with poured fondant icing, I like to frost mine with a sweet buttercream.
For the cookies: Position a rack in the center of the oven and preheat to 375 degrees F. Line 2 half sheet pans (18-by-13-inch baking sheets) with parchment paper.
Combine the flour, sugar, baking powder, salt and lemon zest in your stand mixer bowl fitted with the paddle attachment and mix on low speed to combine. With the mixer on low speed, begin adding in the chunks of butter and mix until the butter has disappeared and the mixture resembles breadcrumbs, about 1 to 2 minutes.
In a liquid measuring cup, whisk to combine the buttermilk, egg, oil and vanilla. With the mixer still on low speed, pour in the liquids and mix until just combined. Stop and scrape the bowl and beater and then mix on low for another 20 seconds until smooth. Scoop the batter into a pastry bag with a 1/2-inch open tip (or a gallon-size freezer bag with a 1/2-inch opening snipped off the corner).
Pipe six 2-inch-wide mounds of dough onto each prepared sheet pan, leaving 2 inches of space around each cookie.
Bake one tray at a time in the center of the oven until the edges are just golden, the centers feel soft but set and a toothpick inserted in the center has a few moist crumbs, 10 to 12 minutes. Let cool completely on the sheet pans, then peel off the parchment paper and frost.
For the frosting: Thoroughly wash and dry your stand mixer bowl and paddle attachment. Beat the butter at medium-high speed until smooth and shiny, 1 to 2 minutes. Add the confectioners' sugar, salt, vanilla and buttermilk. Mix on low speed to combine then increase to high speed and mix for 1 minute. Scrape the bowl and paddle and mix again at high speed until fluffy, about 1 minute.
Transfer about half of the buttercream to a small microwave-safe bowl and set aside. Add the melted chocolate to the remaining buttercream in the mixer bowl. Mix on low speed to combine, scrape the bowl, then mix on high speed for about 10 seconds. Stir with a rubber spatula to incorporate any visible melted chocolate.
Use a small offset spatula to frost half of each cookie with the vanilla buttercream (you’ll use about 2 teaspoons of each frosting per cookie.) Once each cookie is frosted with the vanilla buttercream, frost the other half of each cookie with the chocolate buttercream. Store the cookies in a single layer in airtight containers for up to 3 days.
If the chocolate buttercream stiffens up before you’ve finished frosting your cookies, microwave it for 2 to 3 seconds to soften.