These soft and cakey half-and-half cookies are the perfect palette for your favorite sprinkles, jimmies, confetti, or dragées in elegant shades of black and white.
Preheat oven to 375 degrees. Line 2 baking sheets with parchment paper or silicone baking mats. Sift flour, baking powder, and salt into a medium bowl.
In a stand mixer, beat butter on medium to medium-high speed for several minutes, until smooth. Reduce speed to low and add sugar in a slow stream. Beat butter and sugar on medium-high speed for several minutes until light and fluffy. Beat in vanilla extract, then lemon extract, and then egg whites, mixing to combine after each addition. Add flour mixture and milk in 3 alternating additions and mix until just combined.
Drop ¼-cup scoops of dough about 5 inches apart onto cookie sheets. Moisten a small offset spatula or butter knife with water and spread each mound of dough into a flat 3-inch round. Bake for 8 to 10 minutes, rotating sheets halfway through baking, just until cookie edges start to turn golden.
For the icing, mix confectioners’ sugar, milk, and vanilla in a bowl until smooth. Transfer 1/2 of the icing to another bowl and add cocoa powder. Mix until no cocoa powder lumps remain.
Using a small offset spatula, spread the chocolate icing on half the cookie. Repeat with the vanilla icing on the other half. Return iced cookies to wire racks to set for 30 minutes and then remove them with a spatula. Store cookies in an airtight container, layered between waxed paper, for up to 3 days.