Mix the dry ingredients. In a large mixing bowl, whisk together the 2 cups all-purpose flour, 2/3 cup granulated sugar, 2 tablespoons brown sugar, 1 tablespoon baking powder, 1 tablespoon ground cinnamon, and 1/2 teaspoon kosher salt until evenly combined.
Cut in the butter. Grate the stick of frozen butter directly into the flour mixture using the large holes of a box grater. Gently toss the butter through the dry ingredients until evenly distributed. You can also cube the butter and use a pastry cutter or pastry blender, or pulse the mixture briefly in a food processor. Leave some pea-sized and slightly larger pieces of butter throughout. Whisk the wet ingredients. In a small bowl, whisk together the egg, 1/2 cup heavy cream, and 1 teaspoon vanilla extract until smooth.
Make the scone dough. Pour the wet ingredients into the flour mixture and stir gently with a rubber spatula just until a soft dough forms. Fold in the 1 cup cinnamon chips, if using. Stop mixing as soon as the dry streaks disappear so the scones stay tender. Shape the dough. Turn the dough out onto a clean counter or cutting board and using floured hands gently shape into a 8-inch circle about 1 inch thick. The dough will be sticky but try to use as little extra flour as possible to keep the scones from becoming too tough.
Cut into wedges. Using a bench scraper, sharp knife, or pizza cutter, cut each circle into 8 wedges. Transfer the 8 triangles to a baking sheet lined with parchment paper, spacing them about 2 inches apart. Brush the tops with a little heavy cream and stick the whole baking sheet in the refrigerator to chill for at least 30 minutes. Meanwhile heat the oven to 400°F. Bake in the center of the oven at 400°F for 18–22 minutes, or until the scones are risen and golden brown. Transfer the scones to a cooling rack and let cool for at least 15 minutes.
Make the cinnamon glaze. In a small bowl, whisk together the 1 cup confectioners’ sugar, teaspoon of ground cinnamon, teaspoon vanilla extract, and 2 tablespoons heavy cream or milk until smooth. Add up to the remaining 1 tablespoon heavy cream or milk, a teaspoon at a time, until the glaze is thick but drizzleable.Let the scones cool close to room temperature, then drizzle or brush the cinnamon glaze over the tops.