Preheat the oven to 400°. In a medium bowl, combine the all-purpose and cake flours with the sugar, baking powder, salt and pepper. Cut in the butter until it's the size of large peas. Stir in the cheese and ham and make a well in the center. In a small pitcher, combine the buttermilk and eggs. Pour the liquid into the well and quickly stir until the dough is moistened. Turn the dough out onto a lightly floured work surface and knead 2 or 3 times, just until it holds together.
Pat the dough into a 10-inch round about 3/4 inch thick. Using a 2 1/4-inch round cookie cutter, stamp out biscuits as close together as possible. Gently press the scraps together and stamp out more biscuits. Transfer the biscuits to a baking sheet and brush the tops with buttermilk. Bake for 15 minutes, or until golden and risen. Serve hot.