Preheat oven to 400°F. Line a sheet pan with parchment paper.
In a bowl, combine, the all-purpose flour, wheat flour, oats, baking powder, sugar, and salt. Use a pastry blender or fork to work the butter into the flour mixture. Add the buttermilk and mix gently with a spoon, and then your hands, to bring the mixture together into a ball. Add additional buttermilk a tablespoon at a time, if the mixture is too dry. Do not overwork the dough.
Put the ball of dough onto a lightly floured surface. Gently pat the dough to be about 1 inch tall. Use a 2.5 inch cutter to cut scone rounds. Place the cut scones on the prepared baking sheet. Brush tops with the beaten egg.
Bake until tops are golden, about 18-20 minutes. Serve warm or at room temperature. Scones are best enjoyed the day they are baked, but can be stored at room temperature for a couple of days.
Calories: 266kcal, Carbohydrates: 24g, Protein: 3g, Fat: 19g, Saturated Fat: 11g, Cholesterol: 67mg, Sodium: 172mg, Potassium: 242mg, Fiber: 1g, Sugar: 14g, Vitamin A: 578IU, Calcium: 101mg, Iron: 1mg