Preheat oven to 400°F (200°C) and line a baking sheet with parchment paper.
In a large mixing bowl, whisk together the flour, cocoa powder, sugar, baking powder, and salt until well combined.
Incorporate the cold cubed butter into the dry ingredients using a pastry cutter or two forks until the mixture resembles coarse crumbs.
Fold in the semi-sweet chocolate chips.
Gently stir in the milk and vanilla extract until a soft dough forms; do not overwork the dough.
Drop rounded tablespoons of the dough onto the prepared baking sheet, spacing them approximately 2 inches apart.
Bake for 12 to 15 minutes until the biscuits are set and the bottoms are slightly browned.
Allow the biscuits to cool on the baking sheet for 5 minutes before transferring to a wire rack.