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Mix flour, baking soda and salt in medium bowl. Set aside. Beat sugars and butter in large bowl with electric mixer on medium speed until light and fluffy. Add egg; mix well. Gradually stir in flour mixture on low speed until well mixed. Divide dough in half. Add vanilla and cocoa powder to one half; mix well. Add almond extract to second half; mix well. Press each piece of dough into a 4-inch square. Wrap in plastic wrap. Refrigerate at least 1 hour or until firm.
Roll out cocoa dough into 6x5-inch rectangle. Repeat with almond dough. Using a large sharp knife, cut each rectangle crosswise into 8 strips (3/4-inch wide). Place a strip of each color dough side by side. Top with 2 more strips, alternating colors to create a checkerboard pattern. Lightly press the dough strips together. Repeat with the remaining strips to form 3 more checkerboard dough rectangles. Wrap each in plastic wrap. Refrigerate 2 hours or until firm.
Preheat oven to 350°F. Slice each rectangle into 1/4-inch thick slices. Place 1-inch apart on ungreased baking sheets.
Bake 10 to 12 minutes or until cookies are set. Cool on baking sheets 1 minute. Remove to wire racks; cool completely.