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Preheat oven to 425 degrees F.
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Line 2 baking sheets with parchment paper.
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Place flour, sugar, baking powder, baking soda, and salt in a food processor. Pulse until combined.
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Add the butter and pulse until the ingredients become a crumb texture.
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Pour in buttermilk. Pulse until it forms a sticky dough.
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Add in lemon balm. Pulse until just evenly combined.
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Dump the dough on a lightly floured work surface and knead in the lemon chips.
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Knead a few more times until smooth. Pat into a circle.
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Use a sharp knife to cut the scone dough into triangular pieces and lay them on the baking sheets. Or use a biscuit or cookie cutter to form shapes.
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Brush the tops with more buttermilk.
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Bake until slightly brown, 12-15 minutes.
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Remove from oven and transfer to a wire rack to cool.