Preheat the oven to 350 degrees F. Lightly grease a baking sheet with 1 teaspoon of shortening.
In a large mixing bowl, combine 4 cups flour, baking powder, pepper, salt, ham and cheese. Mix well. Add the remaining shortening and work it into the dry ingredients, using your hands, until the mixture resembles coarse crumbs. Fold in 1 1/2 cups of the milk. The dough with be sticky.
Dust your work surface with 1 tablespoon of the flour. Turn the dough onto the floured surface. Gently fold each side towards the center. Pick up the dough and dust the work surface with the remaining tablespoon flour. Return the dough to the floured surface and fold each side towards the center again. Turn the dough over and light press it out to 1 inch thickness. Cut the biscuits using a 2 1/4-inch round cookie cutter.
Place them on the baking sheet and bake until golden, about 30 minutes. In a medium mixing bowl, whisk the eggs and remaining milk together. Whisk well. Season with salt and pepper. In a large non-stick saute pan, over medium heat, melt the butter. Add the eggs, using a rubber spatula, stir the eggs and cook until the eggs are a soft scramble. Remove from the pan. Slice the biscuits in half and place a spoonful of the eggs in the center of each biscuit.