Preheat oven to 425 degrees. Line a baking sheet with parchment paper.
In a large bowl, whisk together the flour, sugar, baking powder, cinnamon, and salt. Cut in the cold butter pieces with a pastry cutter, until mixture resembles coarse meal.
In a glass measuring cup, measure 1/2 cup milk. Add egg and vanilla extract to measuring cup and whisk together until combined. Pour egg mixture over flour mixture. Using a fork, gently mix until there is no visible flour. Gently stir in cinnamon chips. Mixture will be sticky.
On a well-floured surface, knead mixture a couple times. Use a pizza cutter to cut dough into 12 triangles or squares. Place scones on baking sheet.
Bake for 8 minutes until lightly brown.
Glaze: Whisk together glaze ingredients. Place glaze in a plastic baggie and snip off one of the corners. Drizzle glaze over the cooled scones.