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1
Sift together flour, baking powder, and salt.
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2
With an electric mixer on medium-high speed, cream butter and sugar until pale and fluffy.
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3
Add eggs and vanilla, and beat to combine.
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4
Reduce speed to low.
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5
Gradually add flour mixture, beating until just combined.
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6
Divide dough in half; flatten each half into a disk, and wrap in plastic.
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7
Refrigerate until firm, at least 1 hour (or overnight).
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8
Dough can be frozen, wrapped tightly in plastic and placed in a resealable plastic bag, up to 3 months; thaw overnight in the refrigerator before using.
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9
Let one disk of dough stand at room temperature until soft enough to roll, about 10 minutes.
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10
On a lightly floured work surface (or a piece of parchment paper), roll out dough to just under 1/4 inch thick, adding more flour as needed to keep dough from sticking.
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11
Transfer to a baking sheet; freeze until firm, about 15 minutes.
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12
Preheat oven to 350F, with racks in upper and lower thirds.
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13
Using a 2-inch cookie cutter, quickly cut out shapes from dough (if dough begins to soften, chill in freezer 5 minutes), and transfer shapes to parchment-lined baking sheets, spacing them 2 inches apart, as you work.
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14
Reroll scraps and cut out more shapes.
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15
Brush off excess flour.
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16
Freeze until firm, about 15 minutes.
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17
Repeat with remaining disk of dough.
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18
Bake until edges turn golden, 15 to 18 minutes, firmly tapping down sheets once and rotating them halfway through.
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19
Let cool completely on sheets on wire racks before decorating as desired.
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20
Cookies can be stored up to 1 week at room temperature in an airtight container.