Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a large mixing bowl, cream together the softened butter and granulated sugar until light and fluffy.
Beat in the egg and vanilla extract until well combined.
In a separate bowl, whisk together the flour, baking powder, and salt.
Gradually add the dry ingredients to the wet mixture, mixing until just combined.
Divide the dough in half. To one half, add the cocoa powder and milk, mixing until fully incorporated.
Roll each half of the dough into logs, about 1 inch in diameter. Wrap each log in plastic wrap and refrigerate for at least 30 minutes.
Once chilled, slice each log into 1/4-inch thick rounds. Alternate placing a slice of vanilla and chocolate dough on the baking sheet to create a zebra pattern.
Bake for 10-12 minutes, or until the edges are lightly golden. Allow to cool on the baking sheet for a few minutes before transferring to a wire rack to cool completely.