In a large bowl, mix the flour and salt. Cut in the butter until the mixture resembles coarse crumbs. Gradually add water, tossing with a fork until a dough forms.
Shape the dough into a disk, wrap in plastic wrap, and refrigerate for 30 minutes.
Preheat the oven to 375°F (190°C).
In a separate bowl, beat 1 egg and mix in the grated cheese and black pepper.
In another bowl, beat the remaining egg with milk to create an egg wash.
Roll out the dough on a floured surface and cut into circles. Place a spoonful of the cheese mixture in the center of each circle, then fold the dough over to create a half-moon shape. Seal the edges with a fork.
Place the empadas on a baking sheet, brush with the egg wash, and bake for 20-25 minutes or until golden brown.