Buttery Sugar Cookies

Beat together butter, sugar, and salt in a large bowl with an electric mixer at medium-high speed until pale and fluffy, about 3 minutes in a stand mixer (preferably fitted with paddle attachment) or 6 with a handheld. Beat in egg and vanilla. Reduce speed to low, then mix in flour.
Halve dough and form each half into a disk, then wrap in wax paper. Put each disk in a resealable plastic bag and chill until firm enough to roll into balls, about 1 hour.
Heat oven to 350°F with rack in middle. Line baking sheets with parchment paper.
While oven heats, work with 1 piece of dough (keep remaining dough chilled). Roll 1 level tablespoon of dough into a ball, then roll in coarse sugar in a shallow bowl to coat completely. (If dough becomes too soft to roll easily into balls, quick-chill in the freezer or chill in the refrigerator.)
Place balls 2 inches apart on a lined baking sheet. With the flat bottom of a glass, flatten balls into 2-inch rounds.
Bake cookies, one sheet at time, until bottoms are golden, 12 to 15 minutes total. Cool on sheets 2 minutes, then transfer with a metal spatula to racks to cool completely. Make more cookies with remaining dough on cooled baking sheets.