Beat together butter and sugar in a large bowl with an electric stand mixer at medium until pale and fluffy, about 3 minutes in a stand mixer or 6 minutes with a handheld.

Meanwhile, in a mixing bowl measure and add the flour and salt, set aside.

To the sugar and butter mixture, beat in egg and vanilla. Reduce speed to low and add flour mixture, mixing until just combined.

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.

Place oven rack in middle position and preheat oven to 350° about ten minutes prior to rolling out the dough.

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.

Repeat with remaining dough if desired.

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!