Place the butter and sugar in a large bowl and beat at medium speed until light and fluffy for almost 4 minutes with a hand-held mixer or with paddle attachment if using a stand mixer. Add the eggs one at a time, mix well. Add in the vanilla. When needed, stop the machine during these steps and scrape down the sides of the bowl with a rubber spatula to be sure they are all mixed.
Add the flour and mix until the dough comes together. Divide the dough in half. Place one half on a plastic film and form into a disc or a square.
Add cocoa powder to the dough that stays in the mixer and mix well. Place the cocoa dough on a plastic film and form into a disc or a square as well. Then let them chill for 30-45 minutes in the freezer.
Remove the cocoa dough from the freezer and place it on a parchment paper. If needed, lightly sprinkle cocoa powder over the dough to avoid sticking and roll out into almost 7,5*10,5 inches (19*26cm)long, ⅛ inch (3mm) thick. Set aside.
Take the vanilla dough from the freezer, and place it on a parchment paper. If needed, lightly sprinkle flour over the dough to avoid sticking. Roll out into almost 7,5*10,5 inches (19*26cm)long, ⅛ inch (3mm) thick as you did for the cocoa dough. After these steps, if they are getting too warm, keep them in the freezer for 10 minutes to let them cool-not too much- so you can work easily in the next step.
Flip the vanilla dough with parchment paper over the cocoa dough(if you like you can do the opposite) and slightly press with your rolling pin to stick the doughs to each other. Remove the parchment paper. Make sure two rectangles are the same size, so if needed trim from the edges with a sharp knife.
You can either make these cookies with less or more swirl. Take the long side(less swirl) or short side(more swirl) in front of you and roll the dough tightly to make a cylinder-log. Cover the logs from the sides with the parchment paper and keep in the freezer for almost 1 hour or until ready to cut easily. If you want to keep the log’s rounded shape when you remove it from the freezer-without rolling it to make it round again, place it between two rounded glasses before putting the rounded log in the freezer. (you can check the linked video)
Preheat the oven to 350°F(177C°). Line baking sheet with parchment paper or silicone baking mat.
Remove the log from the freezer. If you don’t use the glass method, and want to make the flatten part round again, you can roll that part on a worksurface a couple of times to give its rounded shape again. Cut the log into ⅕inches (5mm) slices. Place them on the baking sheet almost 2 inches (5cm) apart as they expand during baking and bake for 10 minutes or until the edges of the cookies slightly change color. The cookies will become crunchy as they cool. For soft cookies, you can bake for almost 8 minutes until the cookies set.