Put oven racks in upper and lower thirds of oven, and preheat the oven to 350 degrees F. Pulse peppercorns in grinder until coarsely ground. In a large bowl, whisk together the flour, baking powder, salt, 2 c. cheese, and 1 T. ground black pepper. Blend in the butter with a pastry blender or your fingertips until mixture resembles coarse meal. Whisk 3 eggs with the milk and add to the flour mixture, stirring with a fork until a soft dough forms.
Turn dough out onto a lightly floured surface and quarter the dough. Using well-floured hands, form each piece into a slightly flattened 12-inch long log (about 2 inches wide and 3/4 inch high). Transfer logs to ungreased large baking sheets, arranging logs about 3 inches apart.
Whisk the remaining egg and brush some over the logs, then sprinkle tops of logs evenly with the remaining 1/4 c. cheese and 1/2 T. fresh ground pepper. Bake, rotating the sheets 180 degrees & switching position of the sheets halfway through baking, until logs are pale golden and firm, about 30 minutes total. Remove from the oven. Transfer the logs to wire racks and cool them down to warm, about 10 minutes.
Reduce the oven temperature to 300 degrees F. Carefully transfer 1 warm log to a cutting board and cut diagonally into 1/2 inch thick slices with a serrated knife. Arrange the slices, cut sides down, in 1 layer on a baking sheet. Repeat with remaining logs, transferring the slices to the baking sheets. Bake, turning over once, until golden and crisp, about 35-45 minutes total. Cool biscotti on the baking sheets on racks, for about 15 minutes.
* Biscotti will keep in an airtight container, at room temperature, for 2 weeks.