In a bowl, sift the flour with the sugar, baking powder and salt. In a food processor, pulse the dry ingredients with the butter until the butter is the size of large peas. Transfer the mixture to a large bowl and refrigerate until well chilled, about 30 minutes.
Line 2 baking sheets with parchment paper. In a medium bowl, whisk the cream with the egg. Stir the cream mixture into the dry ingredients until a sticky dough forms. Using a 1/2-cup measure, scoop 5 mounds of dough onto each prepared baking sheet, spacing them well apart. Brush the mounds with the egg wash and refrigerate until chilled, about 20 minutes.
Preheat the oven to 400° and position racks in the upper and lower thirds. Bake the scones for about 30 minutes, until golden and cooked through; shift the sheets from front to back and top to bottom halfway through baking. Let the scones cool on the baking sheets. Serve with the three butters.
The scones can be stored in an airtight container overnight.
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