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.