Black-and-White Cookies

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1. 1Step 1: In a medium bowl, stir together flour, cornstarch, baking powder and salt.
2. 2Step 2: In a large bowl, beat butter and shortening with a mixer on medium 30 seconds. Add granulated sugar. Beat on medium to high 1 minute, scraping bowl as needed. Beat in eggs and egg white. Add flour mixture, beating on low just until combined. Cover and chill dough 2 hours.
3. 3Step 3: Preheat oven to 350 degrees. Line two cookie sheets with parchment paper. Drop dough by 1/4-cup portions 3 inches apart onto prepared cookie sheets. (Dough will be sticky.) With floured fingers, flatten dough portions into 3-inch circles.
4. 4Step 4: Bake until edges are firm and light brown, about 10 minutes. Cool on cookie sheets 5 minutes. Remove; cool on a wire rack.
5. 5Step 5: In a medium bowl, stir together powdered sugar, 3 tablespoons milk, the corn syrup, and vanilla. Transfer 1/2 cup of the mixture to a small bowl; stir in cocoa powder and 1 tablespoon milk. Icing should be a thick glazing consistency. If needed, stir in additional milk, 1/2 teaspoon at a time, to each portion of icing, to loosen.
6. 6Step 6: Spread half of each cookie with white icing. Spread remaining half with chocolate icing. (It's traditional to frost the flat undersides of the cookies, rather than their rounded tops, but either way works.) Let stand until set, about 1 hour.
7. 7Step 7: Place frosted cookies in a single layer in an airtight container. Store in refrigerator up to 3 days or freeze up to 3 months. Let chilled cookies stand at room temperature before serving.