Put oven racks in the upper and lower thirds of your oven and preheat it to 350°F.
In a grinder, pulse the black peppercorns until they are coarsely ground.
In a large bowl, whisk together the flour, baking powder, salt, 2 cups of the cheese, and 1 tablespoon of the ground black pepper.
Blend in the butter using a pastry blender or your fingertips until the mixture resembles coarse meal.
In a separate bowl, whisk together 3 eggs with the milk. Add this mixture to the flour mixture, stirring with a fork until a soft dough forms.
Transfer the dough onto a lightly floured surface and divide it into four quarters.
Carefully transfer the logs to 2 ungreased large baking sheets, spacing them about 3 inches apart.
Whisk the remaining egg and brush some over the logs.
Bake the logs, rotating the sheets 180 degrees and switching their positions halfway through baking.
Reduce the oven temperature to 300°F. Carefully transfer one warm log to a cutting board and cut the log diagonally into ½-inch-thick slices.
Arrange the slices, cut sides down, in a single layer on a baking sheet.
Bake the slices, turning them over once, until they are golden and crisp.
