Preheat the oven to 400°F (200°C) and line a baking sheet with parchment paper.

In a mixing bowl, whisk together the flour, baking powder, salt, and black pepper.

Add the cold, cubed butter to the flour mixture and use a pastry cutter or your fingers to blend until the mixture resembles coarse crumbs.

Stir in the diced ham and shredded cheese until evenly distributed.

In a separate bowl, whisk together the milk and beaten egg, then add to the dry ingredients. Mix until just combined.

Turn the dough onto a floured surface and gently knead it a few times until it comes together.

Pat the dough into a circle about 1 inch thick. Cut into wedges or use a biscuit cutter to make rounds.

Place the scones on the prepared baking sheet and brush the tops with additional milk.

Bake in the preheated oven for 15-20 minutes, or until golden brown.

Remove from the oven and let cool slightly before serving.