Whisk together the flour, baking powder, pepper and salt in a medium bowl. Set aside.
Beat the butter and sugar in a bowl with an electric mixer on medium-high speed until light and fluffy, about 3 minutes. Add the egg and beat to combine. Add the flour mixture and beat on medium-low speed until just incorporated. Stir in the cherries.
Lay out a large piece of plastic wrap and scoop the dough on top. Using the plastic as an aide, form the dough into an even log, about 2 inches in diameter and 10 inches long. Refrigerate until very firm, at least 2 hours and up to overnight.
Position oven racks in the upper and lower thirds of the oven and preheat to 350 degrees F. Line 2 baking sheets with parchment paper.
Unwrap the dough, place it on a cutting board and use a serrated knife to cut it into 1/4-inch-thick rounds. Lay the rounds on the prepared baking sheets about 1 inch apart. Dust very lightly with white pepper.
Bake the cookies until just golden on the bottom and edges, about 12 minutes. Cool on the baking sheets 5 minutes, then carefully transfer to a rack and cool completely. Repeat with any remaining cookies, cooling the baking sheets between batches.