Preheat the oven to 425 degrees F and line a large lipped baking sheet with parchment paper.
Put the flour into a bowl with the baking soda, cream of tartar, and sugar. Chop the butter and the vegetable shortening into pieces and drop them into the flour. Rub the fats into the flour - or just mix any old how - and then pour in the buttermilk, working everything together to form a dough.
Lightly flour your work surface. Pat the dough into a round-edged oblong about 1 3/4 inches thick and cut out 2-inch scones with a biscuit cutter. (Mine are never a uniform height, as I only pat the dough into its shape without worrying whether it's irregular or not.)
Arrange the scones fairly close together on your lined baking sheet, and brush with beaten egg (to give golden tops) or not as you wish.
Bake for 12 minutes, by which time the scones will be dry on the bottom and have a relatively light feel. Remove them to a wire rack to cool, and serve with clotted cream and your favourite jam.
Make Ahead Note: Scones are best on the day they are made but day-old scones can be revived by warming in oven preheated to 300 degrees F for 5 to 10 minutes.
Freeze Note: Baked scones can be frozen in airtight containers or resealable bags for up to one month. Thaw for 1 hour at room temperature and warm as above. Unbaked scones can be put on parchment-lined trays and frozen until solid. Transfer to resealable bags and freeze for up to 3 months. Bake direct from frozen, as directed in recipe, but allowing extra 2 to 3 minutes baking time.