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To make the brown butter: Melt, then cook 5 tablespoons of the butter in a saucepan over medium heat, swirling occasionally, until golden brown. Pour into a heatproof container, cool slightly, then freeze until solid, about 2 hours.
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Preheat the oven to 425°F. Line a baking sheet with parchment.
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Combine the 6-grain blend, flours, baking powder, sugar, and salt until well blended.
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Work both the chilled brown butter and the additional 3 tablespoons butter into the flour mixture until unevenly crumbly.
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Combine the eggs and milk, then mix into the flour-butter mixture.
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Turn the dough out onto a floured surface and pat it into an 8" disk. Cut into 8 wedges and place on the baking sheet.
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Bake the scones for 15 to 18 minutes, until golden. Cool slightly before glazing.
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To make the glaze: Brown the butter as you did for the scones, then combine all the ingredients, adding enough milk to make a spreadable glaze. Glaze scones while still warm, and serve.
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Store any leftover scones well-wrapped, at room temperature, for several days. Freeze for longer storage.