Preheat the oven to 375 degrees F. Whisk the flour, baking powder, baking soda and sugar together in a bowl. With your fingers or a fork, cut in the butter until mixture forms pea-sized crumbles. Mix in the cheese, ham and parsley. Gently mix in buttermilk/egg mixture until a loose dough forms, and then turn onto a floured surface. Shape into a ball, and then flatten into a 1-inch thick disc. Cut into 3-inch rounds and place on a baking sheet. Bake in the middle of the oven 18-20 minutes, until puffed and golden.