Cream the Butter and Sugar: In a stand mixer fitted with a paddle attachment (or by hand), beat the butter and granulated sugar on medium-high speed until light and fluffy, about 3 minutes.
Add Wet Ingredients: Add the 22g sourdough starter and the egg. Beat until well combined.
Incorporate Dry Ingredients: In a separate bowl, whisk together the flour, cocoa powder, baking soda, baking powder, and salt. Gradually beat the dry ingredients into the wet mixture until just combined.
Ferment the Dough: Cover the dough tightly and let it ferment at room temperature for 8-12 hours, or overnight. If you need to refrigerate it, you can do so for up to 24 hours after fermentation. Before baking, bring the dough back to room temperature for 1-2 hours.
Preheat and Shape: Preheat your oven to 350°F (177°C). Roll the dough into small balls, about 12-14 cookies worth. Flatten each dough ball slightly on a parchment-lined baking sheet to help them spread into thin cookies.
Final Chill: Chill each tray of flattened cookie dough for at least 15 minutes in the fridge or 10 minutes in the freezer before baking.
Bake the Cookies: Bake for 8-12 minutes, or until the edges are firm and slightly crisp. Remove from the oven and allow them to cool completely on the baking sheet.