1. Put oven racks in the upper and lower thirds of the oven and preheat it to 350°F.
2. Pulse the black peppercorns in a grinder until coarsely ground.
3. In a large bowl, whisk together the flour, baking powder, salt, 2 cups of the Parmigiano-Reggiano, and 1 tablespoon of ground black pepper. Blend in the butter with a pastry blender or your fingertips until the mixture resembles coarse meal.
4. In another bowl, whisk 3 eggs with the whole milk and then add to the flour mixture, stirring with a fork until a soft dough forms.
5. Turn the dough onto a lightly floured surface and quarter it. Using well-floured hands, form each piece into a slightly flattened log that is 12 inches long, about 2 inches wide, and ¾ inch high.
6. Whisk the remaining egg and brush it over the logs. Sprinkle the tops evenly with the remaining ¼ cup of Parmigiano-Reggiano and ½ tablespoon of ground pepper.
7. Bake the logs, rotating the sheets 180 degrees and switching their positions halfway through, until they are pale golden and firm, about 30 minutes total.
8. Cool the logs on the sheets for about 10 minutes before transferring them to a cutting board.
9. Reduce the oven temperature to 300°F. Carefully transfer one warm log to a cutting board and cut diagonally into ½-inch-thick slices using a serrated knife.
10. Arrange the slices cut sides down in a single layer on a baking sheet. Repeat with the remaining logs.
11. Bake the slices, turning them over once, until golden and crisp, which will take about 35 to 45 minutes total.
12. Cool the biscotti on the baking sheets on racks for about 15 minutes before serving.