These are classic cake based cookies, a speciality of New York City

Preheat oven to 375°. To prepare cookies, lightly spoon flour into dry measuring cups; level with a knife. Combine flour, baking powder, and salt, stirring with a whisk. Place applesauce in a fine sieve; let stand 15 minutes. Combine drained applesauce, granulated sugar, and butter in a large bowl; beat with a mixer at medium speed 2 minutes or until well blended. Beat in vanilla and egg whites. Add flour mixture; beat at low speed until blended. Drop dough by tablespoonfuls 2 inches apart onto parchment-lined baking sheets. Bake at 375° for 10 minutes or until set (not browned). Cool on pans 2 minutes or until firm. Remove from pans; cool completely on wire racks. To prepare frosting, combine 3/4 cup powdered sugar, 1 tablespoon milk, and almond extract in a bowl, stirring well with a whisk until smooth. Working with 1 cookie at a time, hold cookie over bowl and spread about 1 teaspoon white frosting over half of cookie (scrape excess frosting from edges). Let stand 10 minutes or until frosting is set. Combine 3/4 cup powdered sugar and cocoa in a bowl. Gradually add 2 tablespoons milk, stirring with a whisk until smooth. Working with 1 cookie at a time, hold cookie over bowl and spread about 1 teaspoon chocolate frosting over other half of cookie (scrape excess frosting from edges). Let stand 10 minutes or until frosting is set.