Beat softened butter and powdered sugar for about 2 minutes until smooth and creamy. Avoid whipping excessive air into the mixture.
Mix in vanilla and salt. Add flour in two additions on low speed, stopping when the dough forms soft clumps.
Press the clumps together by hand without kneading. Shape into two logs about 1 1/2 inches wide, then wrap firmly.
Refrigerate for 1 hour, until firm enough to slice. Heat the oven to 325°F (165°C) and line two baking sheets.
Cut logs into 24 rounds, about 1/2 inch thick. Rotate each log between cuts to help keep the slices round.
Arrange slices 1 inch apart and bake for 16–20 minutes. Look for dry surfaces and pale golden edges rather than dark browning.
Leave on the sheet for 10 minutes because fresh shortbread is fragile. Transfer carefully to a rack to cool completely.
Serve once cool and crisp. Store in a tightly closed container after all warmth has escaped, separating layers with parchment if desired.
