Heat the oven to 350°F/175°C. Line two baking sheets with parchment paper.
In a mixing bowl, cream the butter with both sugars until smooth and cohesive. Add the egg and vanilla and mix until fully incorporated.
In a separate bowl, whisk together the flour, cocoa powder, baking soda, and salt. Add to the butter mixture and mix just until a uniform dough forms. Fold in the chocolate.
Portion the dough into 27 balls and arrange on the prepared sheets. Freeze for at least 1 hour.
Bake, spacing cookies well apart, until the edges are set and the centers remain soft, 7 to 10 minutes. Sprinkle lightly with flaky salt and let cool completely before serving.