Preheat your oven to 350°F (175°C).
In a bowl, beat the softened butter and granulated sugar together until fluffy.
Add the egg and vanilla extract to the creamed mixture and mix well.
In a separate bowl, whisk together the flour, cocoa powder, and salt.
Gradually add the dry ingredients to the butter mixture, mixing until just combined.
Divide the dough in half. To one half, add the cocoa powder and mix thoroughly.
Roll out both dough halves between sheets of parchment paper into rectangles.
Layer one rectangle on top of the other, then gently roll them into a log.
Wrap the log in plastic wrap and refrigerate for at least 30 minutes.
Slice the log into 1/4-inch rounds and place them on a baking sheet lined with parchment paper.
Bake in the preheated oven for 10-12 minutes or until the edges are set.
Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack.