In a mixing bowl, cream together 100g of soft butter and 50g of powdered sugar until light and fluffy. Add in 50g of starch, 140g of flour, 1 large egg, and 1 teaspoon of vanilla extract. Mix until fully combined, then set aside.
In another bowl, cream 100g of soft butter with 50g of powdered sugar. Add 50g of starch, 120g of flour, 20g of black cocoa, and 1 large egg. Mix until the chocolate dough comes together.
Take a portion of the light dough and flatten it on a piece of parchment paper. Do the same with the chocolate dough. Place the chocolate dough on top of the light dough and gently roll them together to form a log.
Wrap the dough log in parchment paper and refrigerate for at least 30 minutes.
Preheat your oven to 180°C (350°F). Once chilled, remove the dough from the refrigerator and slice into rounds about 1/2 inch thick.
Place the cookie slices on a baking sheet lined with parchment paper, leaving space between each cookie. Bake for 10-12 minutes, or until the edges are set and the tops look slightly puffed.
Allow the cookies to cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.