In a large bowl, cream together the softened butter and sugar for both doughs until light and fluffy.

For the vanilla dough: Add the egg yolk and vanilla extract. Gradually mix in the flour until a soft dough forms. Wrap in plastic and chill for 30 minutes.

For the chocolate dough: Add the egg yolk, vanilla extract, and cocoa powder. Gradually mix in the flour until combined. Wrap in plastic and chill for 30 minutes.

On a lightly floured surface, roll out the vanilla dough into a 9x12-inch rectangle. Repeat with the chocolate dough.

Carefully place the chocolate dough on top of the vanilla dough. Gently press together and trim edges to make even.

Starting from the long side, tightly roll the dough into a log. Wrap in plastic and refrigerate for at least 1 hour or until firm.

Preheat oven to 350°F (175°C). Line baking sheets with parchment paper.

Slice the log into 0.25-inch thick rounds and place them 2 inches apart on the prepared baking sheets.

Bake for 10–12 minutes, or until edges are lightly golden. Cool on the baking sheet for 5 minutes before transferring to a wire rack.