With the rack in the middle position, preheat the oven to 180 °C (350 °F). Line two baking sheets with parchment paper.
In a bowl, combine the flour, cocoa powder, and salt. Set aside.
In another bowl, cream the butter and sugar with an electric mixer. At low speed, add the dry ingredients and stir until smooth. If the dough seems too dry, add milk, as needed. Form into a disc with your hands. Cover with plastic wrap. Refrigerate for about 30 minutes.
On a generously floured work surface, roll out the dough into a 3-mm (1/8-inch) thick sheet. Cut out twenty cookies using the model. Place the cookies on the baking sheets. Bake one sheet at a time for about 12 minutes.
Gently mount both parts of the tree to get a three dimensional cookie.