Half-Moon Cookies

Preheat oven to 350 degrees. Whisk together flours, baking soda, and salt in a bowl. In another bowl, beat butter on medium speed until smooth, about 2 minutes. Add 1/2 cup granulated sugar and beat until light and fluffy, about 3 minutes. Beat in egg and vanilla. Add flour mixture in 3 batches, alternating with 2 additions of buttermilk, beating until just combined (do not overmix). Refrigerate dough until firm, about 1 hour.

Roll 1- or 1 1/2-tablespoon pieces of dough into balls; place 2 inches apart on parchment-lined baking sheets. Bake until bottoms turn golden, rotating sheets halfway through, about 10 minutes. Transfer cookies to wire racks; let cool completely. Cookies can be stored at room temperature up to 1 day.

Cook berries and remaining 1 tablespoon granulated sugar in a small saucepan over medium-high heat, stirring and crushing berries until soft and juices have been released. Pass mixture through a fine sieve into a bowl, pressing on solids to extract as much liquid as possible, and let cool completely.

Whisk together confectioners' sugar, honey, lemon juice, and 2 tablespoons water in a small bowl. Transfer half of icing to another bowl, and whisk in 1 teaspoon more water. Divide remaining portion in half again, and stir 1/2 teaspoon berry puree into one part, and cocoa powder and 3/4 teaspoon water into other. Spread white icing on half of each cookieâ??s flat side and fruit or chocolate icing on other half. Let set 30 minutes before serving.