Preheat the oven to 425 degrees. Spray baking sheets with non stick spray, or line with silicone liners; set aside.
Whisk together flour, sugar, salt, baking powder, nutmeg, and cinnamon in a large bowl.
Grate in the cold butter. (or cut it in with a pastry cutter) Stir in the cinnamon chips.
In a small bowl, whisk together the egg, vanilla, and eggnog. Gently stir into the dry ingredients till just moistened . Knead gently till dough comes together.
Divide dough in half. On a lightly floured counter, press each half into a 6 1/2" circle about 3/4" thick. Cut each circle into 6 wedges.
Place scones on lightly greased cookie sheets about an inch apart. Brush each scone with milk. Bake at 425° for about 15 minutes or till lightly browned.
For glaze: whisk together all ingredients in a small bowl, adding enough eggnog till it is about the consistency of very heavy cream. Drizzle over warm scones.