Refrigerate a metal bowl for 5 minutes to get it cold.
Preheat the oven to 425 degrees.
In the refrigerated bowl, add the flour, baking soda, cream of tartar, sugar and salt. Cut the cold butter into small cubes and add to the flour mixture. Using a pastry cutter, cut the butter in with the flour mixture until the butter is mostly mixed in. It is okay if there are small pieces of butter.
Make a well in the flour, in the center of the bowl. Add the egg and buttermilk to the well. Using a wooden spoon, mix the wet ingredients into the dry ingredients. Mix just until blended, being careful not to overmix. Fold in the cinnamon chips.
Put about 1/4 cup of flour on the cupboard. Turn the dough out onto the floured counter. Turn it over so the floured side is up. Make a disk that is about 1 1/4 inches thick. Use a knife to cut the disk into 8 triangles, as if you were cutting a pie. Place the scones on a greased cookie sheet, or a nonstick baking mat.
Bake immediately for 12 minutes. Allow the scones to cool for 3-5 minutes and prepare the glaze.
In a small bowl, melt the 3 tablespoons of butter. Add in the powdered sugar and vanilla. Mix well. If needed, add 1-2 tablespoons of milk in order to easily spoon the glaze over the scones.
Glaze the top of the scones. The glaze will run over the sides of the warm scones.
The calories shown are based on the recipe making 8 scones, with 1 serving being 1 scone. Since different brands of ingredients have different nutritional information, the calories shown are just an estimate. **We are not dietitians and recommend you seek a nutritionist for exact nutritional information.**