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To make the dough: In a large bowl, whisk together the flour, sugar, salt, pepper, and baking powder.
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Work in the butter just until the mixture is unevenly crumbly; it's OK for some larger chunks of butter to remain unincorporated.
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Add the grated cheese and mix until evenly combined.
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In a separate bowl, whisk together the eggs and milk.
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Add the liquid ingredients to the dry ingredients. Using a bowl scraper or a large spoon, stir until everything is moistened and holds together. If the mixture seems dry, drizzle in additional milk about a teaspoon at a time until the dough comes together.
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Line a baking sheet with parchment; if you don't have parchment, just use the pan without greasing it. Sprinkle a bit of flour atop the parchment or pan.
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To shape the scones: Scoop the dough by the 1/4-cupful onto the baking sheet. (A scone scoop is helpful here.)
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Brush the tops of the scones with milk and sprinkle with additional cheese and a bit of black pepper, if desired.
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For best texture and highest rise, place the pan of scones in the freezer for 30 minutes, uncovered. Chilling the scones relaxes the gluten in the flour, making the scones more tender and allowing them to rise higher. It also chills the fat, which makes the scones a bit flakier. While the scones are chilling, preheat the oven to 425°F with a rack in the upper third.
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To bake the scones: Bake the scones in the upper part of the oven for 18 to 20 minutes, or until they're a light golden brown.
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Remove the scones from the oven and cool briefly on the pan. Serve warm; they're delicious as is and extra-tasty with a pat of salted butter on top.
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Storage information: When the scones are completely cool, wrap and store them at room temperature for up to several days. To reheat room-temperature scones, place them on a baking sheet, tent lightly with foil, and warm in a preheated 350°F oven for about 10 minutes.