In the bowl of your food processor, combine the flour, cacao powder, and icing sugar. Pulse the mixture to ensure it's well combined and free of any lumps.
Add the very cold butter, which should be cut into small cubes, to the dry ingredients in the food processor. Pulse the mixture until it resembles fine crumbs.
Once you have the crumbly texture, add the whisked egg to the mixture in the food processor. Pulse again until a sticky dough begins to form. You should be able to press the crumbs together, and they should stick.
Gather the pastry dough into a disk shape and place it between two sheets of baking paper). Roll the dough out into a large circle, approximately 3mm (or 1/8 inch) thick.
Transfer the rolled-out dough to the fridge and let it rest for at least 1 hour, or you can leave it for up to 24 hours to chill before using.
Remove the baking paper from the pastry and use a round or fluted cookie cutter to cut out rounds of pastry dough. Gently place these pastry rounds into the openings of a muffin pan, lightly pressing the edges between the bottom and sides to remove any air bubbles. Use a fork to prick the bottom of each pastry round. Return the muffin pan to the fridge and let the pastry rest for at least 1 hour, or up to 24 hours.
Preheat your oven to 160°C/325°F. While the oven is heating up, place the muffin pan with the pastry in the freezer to chill.
Line each tartlet shell with a small piece of crumpled baking paper and fill them with baking weights, dry beans, or rice to prevent the pastry from puffing up during baking. Bake the tartlet shells in the preheated oven for 15 minutes. Then, remove the baking weights and baking paper and bake for an additional 15 minutes or until the pastry is fully baked. Allow the tartlet shells to cool completely before using them.