Preheat the oven to 400 degrees and line a baking sheet with parchment paper. In a food processor, combine the flour, cocoa powder, brown sugar, baking powder, baking soda and salt. Add the pieces of butter and pulse until coarse crumbs form. Transfer to a large bowl and stir in the chocolate chips.
In a small bowl, mix the egg with the buttermilk until just combined. Add to the dry ingredients and stir until the dough just comes together.
Divide the dough into 2 equal parts and place on the prepared baking sheet. With lightly floured hands, shape each piece into a flat, round cake about 6 inches in diameter. Using a sharp, straight-edged knife, cut each round into 6 equal wedges, leaving them in place. Sprinkle the tops with the granulated sugar and bake until firm in the center when lightly touched, 20 to 25 minutes. Transfer to a rack and let cool slightly before breaking into wedges.
In a small bowl, using a hand mixer or a fork, beat the softened butter with the confectioners sugar, vanilla and cinnamon until light and fluffy. Serve with the warm scones.
