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1
Whisk together flour, baking powder, and salt in a small bowl.
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2
Beat together butter and sugar in a large bowl with an electric mixer at medium-high speed until pale and fluffy, about 3 minutes in a standing mixer (preferably fitted with paddle attachment) or 6 with a handheld.
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3
Beat in egg and vanilla.
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4
Reduce speed to low, then add flour mixture and mix until just combined.
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5
Form dough into a 12-inch log (2 inches in diameter) on a sheet of plastic wrap and roll up dough in plastic wrap.
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6
Chill dough on a baking sheet until firm, at least 4 hours.
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7
(To roll cookies into balls, see cooks' note, below.)
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8
Put oven racks in upper and lower thirds of oven and preheat oven to 375F.
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9
Cut enough 1/8- to 1/4-inch-thick slices from log with a heavy knife to fill 2 ungreased large baking sheets, arranging slices about 1 inch apart (chill remainder of log, wrapped in plastic wrap).
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10
If garnishing with coarse sugar, sprinkle slices with it.
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11
Bake cookies, switching position of sheets halfway through baking, until edges are golden, 12 to 15 minutes total.
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12
Cool on sheets 3 minutes, then transfer with a metal spatula to racks to cool completely.
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13
Make more cookies with remaining dough on cooled baking sheets.
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14
*Available at specialty foods shops and New York Cake & Baking Distributor (800-942-2639).