Preheat the oven to 350 degrees Fahrenheit. Line a baking sheet with a silicone baking mat or parchment paper.
In a large bowl whisk together the flour, sugar, brown sugar, baking powder and salt. In a liquid measuring cup whisk together the egg and milk. Refrigerate until ready to use.
Grate the frozen butter into the dry mixture and work it into the flour mixture with your fingers or a pastry cutter. Add cinnamon chips.
Add milk mixture to flour mixture and mix together until you can form it into a ball. Try not to work the mixture too much.
Dust a work surface with gluten free flour and cut the ball in half. Form each half into a 5 ½ inch wide disk. Cut each disk in half vertically and then cut each side into three triangles. You should have 12 scones.
Bake 6 scones at a time on a parchment or silpat lined sheet pan. Whisk an egg in a small bowl and brush each scone with the egg wash and sprinkle with sugar.
Bake for 18 minutes or until slightly brown on top and crackly.