Preheat your oven to 350 degrees and line a baking pan with parchment paper.
In a large bowl, whisk together flour, baking powder, salt, 1 ½ tsp pepper, and 2 cups of grated cheese. With your fingers or a pastry cutter, blend in butter until coarse crumbs form.
In a small bowl, whisk together 2 eggs and milk. Make a well in the center of your dry ingredients and add egg mixture. Use a wooden spoon to gently combine until a sticky dough forms.
Sprinkle some flour on a large cutting board or your clean countertop and transfer the dough on top. Shape your dough into a 12” long log, gently flatten to about ¾” thickness and 2 ½ inches wide. Transfer to your prepared baking pan.
Whisk the remaining egg in a small bowl and brush on top of the dough. Sprinkle with reserved ½ cup grated cheese and ½ tsp black pepper. Bake for 30-35 minutes or until golden brown.
Reduce oven temperature to 300 degrees. Let the par-baked biscotti dough cool for 10 minutes and then carefully transfer to a cutting board. Use a serrated knife to slice on a slight diagonal into ~16 slices.
Place individual biscotti back on the prepared sheet, cut side down, and bake for an additional 40-45 minutes or until crisp, flipping the individual biscotti midway through cooking for even browning on both sides. Let cool on the baking sheet or a rack. Store at room temperature in a sealed container for up to a week.