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1
Start off by whisking together flour and salt in a small bowl. Set aside.
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2
Beat together butter and sugar in a large bowl with an electric mixer on medium speed until pale and fluffy. This will take about 3 minutes in a stand mixer or 6 minutes with a handheld. Beat in egg and vanilla. Reduce speed to low and add flour mixture, mixing until just combined.
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3
Form dough into 2 balls and flatten each into a 6-inch disk. Chill disks, wrapped in plastic wrap, until firm, at least 1 hour.
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4
Place oven rack in middle position and preheat oven to 350 degrees (F) about ten minutes prior to rolling out the dough.
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5
Roll out 1 disk of dough (keep remaining dough chilled) into an 8 1/2-inch round (1/4 inch thick-ish) on a well-floured surface with a well-floured rolling pin. (If dough becomes too soft to roll out, rewrap in plastic and chill until firm.) Cut out as many cookies as possible from dough with cookie cutters and transfer to 2 ungreased large baking sheets, arranging cookies about 1 inch apart.
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6
Repeat with remaining dough if desired (or you can save the second disk for later).
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7
Bake cookies, 1 sheet at a time, until edges are golden, 8 to 10 minutes, then transfer to racks to cool completely. Chill the cookies that are waiting to be baked!
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8
MAKE AHEAD: Dough can be chilled for up to 3 days. Cookies keep, layered between sheets of wax paper or parchment, in an airtight container at room temperature 1 week.
