Preheat oven to 425 F. Line a baking sheet with parchment paper.
Sift the dry ingredients (cocoa powder, sugar, baking powder, baking soda, and salt) into a large bowl.
Add the butter to the bowl and use a pastry cutter to cut the butter into the flour mixture.
In a small bowl, whisk together the wet ingredients (egg, milk, and vanilla). Pour the wet ingredients into the flour-butter mixture and use a fork to stir the mixture together until the dough begins to form.
Add the chocolate chips and continue stirring with a fork until a dough ball forms. If the dough seems too dry, add milk by the teaspoonful.
Once the dough forms, pour it out onto a pastry mat or well-floured kitchen counter and knead several times until the dough is fully formed.
Divide dough in half and pat each half into a 6-inch circle, roughly 3/4 inch thick. Use a sharp knife or a pastry cutter to cut each circle into six portions.
Spread the wedges out across the prepared baking sheet. Bake scones 18 to 23 minutes until set.
Remove from oven and let cool on baking tray for 5 minutes, before removing to a wire rack to fully cool.
While the scones cool, whisk together the confectioners' sugar and milk in a small bowl until a thick icing forms. Add more sugar or milk as needed to achieve the correct consistency.
Once the scones are cool, drizzle with frosting to make the most decadent of breakfasts!