
Preheat oven to 425 degrees. Grease a large baking sheet. In a bowl, whisk together the flour, baking powder, paprika, sugar, salt, pepper, and dry mustard. Incorporate the butter with a pastry blender or two knives just until mixture resembles coarse crumbs. In a small bowl, whisk together the eggs and 1/2 cup of milk and stir it into the flour mixture. Stir in the ham, 1/2 cup of the cheese, and the scallions (dough will be very sticky). Turn the dough out onto a lightly floured surface, roll it into a ball, then flatten into a disk. Gently pat out the dough into a 10-inch round, about 1/2 inch thick. Cut the round into 8 wedges using an oiled knife or a pizza wheel.
Transfer the scones to the baking sheet. Brush tops with the remaining milk, and sprinkle with the remaining cheese. Bake scones, rotating baking sheet halfway through cooking, until golden, 15 to 17 minutes. Cool and serve immediately, or freeze each scone wrapped in foil and put in an airtight container. To reheat, let the foil-wrapped scones stand at room temperature while oven preheats to 350 degrees. Warm scones, still wrapped, 15 minutes.