Before You Start
Preheat the oven to Bake 375°F.
In a large bowl, combine flours, salt and baking powder and stir with a fork. Add the butter and, using a pastry cutter or hands, work into the dry ingredients until the butter is pea-sized and well-incorporated.
Add the ham, cheese and chives, and stir with a fork. In a large measuring cup, mix cream with eggs. Add the cream mixture to the bowl and stir with a fork. Use your hands to pull the dough together and knead gently to form into a large disc. Chill the dough for 10 minutes. Use your hands to form the dough into small (2-inch) spheres, about 16 scones. Place half the scones on a baking sheet and press down on scones to flatten slightly.
Egg wash and cheese topping
In a small bowl, combine egg and heavy cream and stir with a fork. Brush the scones all over with egg wash. Sprinkle with cheese.