Cream together butter and powdered sugar in a bowl until light and fluffy. Add vanilla extract and mix well. Gradually incorporate all-purpose flour until a soft dough forms. Shape into a disk, wrap, and chill for at least 30 minutes.

In the same bowl, beat butter and powdered sugar until creamy. Stir in peppermint extract. Gradually mix in cocoa powder and all-purpose flour until clumpy. Shape into a disk, wrap, and chill for another 30 minutes.

Roll out each dough between parchment paper into a 9-by-12 inch rectangle. Tear chocolate dough into pieces and layer on top of vanilla dough for marbling.

Fold and twist the two layers of dough together, then shape into a log. Wrap tightly and chill in the refrigerator until firm.

Preheat oven to 350°F. Slice the chilled dough into ¼-inch rounds and arrange on a lined baking sheet. Bake for 16-20 minutes until edges are golden. Let cool before transferring to a wire rack.