In a bowl, place two discs of cookie dough. Add cocoa powder and cinnamon. Mix dough by hand until smooth. Shape into two discs. Refrigerate for 1 hour.
On a lightly floured surface or between two sheets of parchment paper, roll out one disc of plain cookie dough at a time into a 30 x 23-cm (12 x 9-inch) rectangle, about 5-mm (¼-inch) thick. Do the same with cocoa and cinnamon cookie dough discs. Layer 2 sheets, one with each dough. Roll a cookie log from the longer side.
Repeat with other two rolled-out dough. Refrigerate both logs for 1 hour
With the rack in the middle position, preheat the oven to 180 °C (350 °F). Line a baking sheet with parchment paper or a silicone mat.
On a lightly floured work surface, cut rolls into 5-mm (¼-inch) thick cookies. Place on the baking sheet, spacing them evenly.
Bake one sheet at a time for about 12 minutes or until lightly browned. Let cool completely.