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Heat oven to 400 degrees with a rack in the upper third. Line a baking sheet with parchment paper.
Whisk flour, sugar, baking powder and salt in a large bowl. Using the large holes of a box grater, grate butter directly into the dry ingredients, stopping a few times along the way to toss the butter pieces into the flour. Use your fingers to work the butter into slightly smaller pieces. Add cherries and toss to combine.
In a small bowl, whisk together sour cream and milk. Add to the flour mixture, and use a fork to stir until all the dry flour bits are incorporated, but the dough is still shaggy. Smoosh and knead the dough a few times until it barely holds together, then dump the dough out onto a lightly floured work surface.
Pat dough to a 1-inch-thick rectangle. Cut into 8 squares, transfer to the prepared sheet, and brush the tops with beaten egg.
Bake until golden brown, 18 to 22 minutes. Let cool slightly. Scones will keep, covered at room temperature, for 3 days. Reheat, if you like, in a toaster oven or at 350 degrees until warmed through.