Preheat the oven to 400ºF. Line a baking sheet with a silicone baking mat or parchment paper (not wax paper). Set aside.
In a large bowl, whisk together the flour, 1/4 cup of the granulated sugar, brown sugar, baking powder, salt, and 1 teaspoon of the ground cinnamon. Quickly grate the frozen butter into the flour mixture. Using a pastry blender, a fork, or two knives, blend the butter into the flour until it resembles coarse crumbs. Set aside.
In a small bowl, whisk together the buttermilk and the egg. Pour this mixture evenly over the flour/butter mixture and blend together with a spatula until everything is just moist. Gently fold in the mini cinnamon chips, using your hands if necessary.
With your hands, form into a ball and transfer to prepared baking sheet. Press ball into 8" disc and cut into 8 equal triangles with a sharp knife. Sprinkle with a mix of remaining granulated sugar and ground cinnamon.
Bake for 22-24 minutes or until edges start to brown. Remove from oven and allow to cool on baking sheet for a few minutes. Scones are best served immediately, but will stay fresh in an airtight container at room temperature for 2 days. Scones may be frozen up to 3 months. Defrost at room temperature and warm to preference before enjoying.