In mixer with paddle attachment, cream butter until smooth.

Add sugar and salt, and mix on medium-low until fluffy, about 2 minutes.

Add vanilla, mix on low until incorporated, about 30 seconds.

Add flour in two parts, mixing on low until incorporated before adding the next, 15 to 30 seconds.

Remove from bowl, shape into a 5-inch square, wrap and refrigerate 2 hours.

Preheat oven to 325°F. Adjust oven racks to lower and upper third. Line two baking sheets with parchment or silicone baking mats.

Place dough between two sheets of plastic wrap. Roll out to a 9-inch square. If dough has become soft, refrigerate until firm.

Cut into 1 1/2-inch squares. Dust with granulated sugar. Transfer to lined baking sheets, leaving 3/4-inch space between each shortbread.

Bake 17-19 minutes, rotating sheets, top to bottom and front to back, halfway through, until shortbread is a light golden brown.

Cool on baking sheets for 10 minutes, then transfer to a rack to cool completely.