||Preheat oven to 400°. Line or lightly grease 2 baking sheets and set aside.
In a large bowl, combine flour, sugar, baking powder, baking soda, and salt. Cut in the butter with a pastry blender until the mixture resembles coarse meal. (Alternately, use a food processor with a metal blade to cut in the butter.) Stir in cinnamon and chopped apples. Do not overwork the dough.
Add 1 & 1/4 cups of buttermilk. Mix until combined and the dough begins to stick together. Add remaining buttermilk if dough is too dry.
Turn the dough out onto a lightly floured work surface. Roll or pat dough into two 6-inch rounds about 1 & 1/2 inches thick. Cut each round in half, then cut each half into 3 triangles. Place on baking sheets.
Mix together beaten egg and milk. Brush the tops of the triangles with egg wash. Then, sprinkle with cinnamon sugar. Bake 25 to 30 minutes, or until golden brown and firm to the touch. Serve immediately.