In a large bowl, cream the softened butter and sugar together until light and fluffy.
Add the egg yolk, milk, and vanilla essence, and mix until well combined.
Gradually sift in the all-purpose flour and baking powder, mixing until a soft dough forms.
Divide the dough into two equal portions.
Leave one portion as is for the vanilla layer.
To the second portion, add the cocoa powder mixture (cocoa powder, milk, and melted butter) and knead until evenly incorporated.
Roll out the vanilla dough into a rectangle on a lightly floured surface.
Do the same for the chocolate dough. Try to make them roughly the same size.
Place the chocolate dough on top of the vanilla dough. Gently press to stick them together.
Starting from one edge, roll the layered dough tightly into a log shape. Wrap it in plastic wrap and freeze for at least ½ hour to firm up.
Preheat your oven to 325°F (160°C) and line a baking sheet with parchment paper.
Remove the dough from the freezer and slice it into ¼-inch thick rounds. Arrange the cookies on the baking sheet, leaving a little space between each.
Bake for 15-20 minutes or until the edges are slightly golden.Allow the cookies to cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.