Preheat oven to 375 degrees F. Line a baking sheet with parchment paper.
In a large bowl, whisk together the flour, cocoa powder, sugar, baking powder, baking soda, and salt.
Grate the butter on the large holes of a box grater, then add to the flour mixture and cut in with a pastry cutter until it resembles crumbs or small peas. Add the chocolate chips and toss to coat.
In a separate bowl, whisk together the milk, eggs, and vanilla extract. Add to the dry ingredients, stirring with a spatula to evenly moisten. The dough will be very shaggy.
Turn the scone dough out onto a large piece of parchment paper. Use the parchment paper to squeeze the scone dough into a ball, pressing and kneading until it comes together. Divide into two pieces and pat them into two 6-inch discs that are roughly ¾" to 1" thick. Use a pastry cutter or sharp knife to cut each disc into 6 wedges for 12 scones.
Arrange the scones on the parchment lined baking sheet. Bake for 18-22 minutes, just until done. Cool.
While the scones cool, whisk the powdered sugar, cocoa powder, milk, and vanilla extract together to form a glaze. Drizzle over the scones. The glaze will set after 20-30 minutes.