Preheat the oven to 400 degrees F. Line a rimmed baking sheet with parchment paper.
Put the flour, oats, baking powder, sugar, 1 teaspoon salt and 1/4 teaspoon pepper in a food processor; pulse until the oats are finely ground. Add the butter and pulse until the mixture resembles a coarse meal. Pour into a large bowl and form a well in the center. Gently stir in the buttermilk until the dough just comes together.
Dust a work surface with flour. Turn the dough out onto the floured surface. Flatten the dough into a rectangle about 1 inch thick. Fold the dough in thirds, like a letter. Flatten and repeat from the other direction. Roll or pat out to a generous 3/4-inch thickness. Cut out rounds using a 2- to 3-inch biscuit cutter, rerolling and cutting the scraps. Arrange on the prepared baking sheet, leaving 1 1/2 to 2 inches between the biscuits. Brush the tops with buttermilk.
Bake the biscuits until risen and light golden, 15 to 18 minutes. Serve warm or at room temperature.
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