In a large bowl using a handheld mixer or a stand mixer fitted with a paddle attachment, beat the butter and brown sugar together on medium-high speed until completely smooth and creamy.
Add the vanilla and beat until combined.
Add the flour and salt and beat on low speed until incorporated.
Turn the mixer up to medium-high speed and beat until the dough comes together.
If the dough is too crumbly and won’t come together after a couple minutes of beating, stop the mixer, pour the dough crumbles on a work surface, and use your hands to bring it together.
With lightly floured hands, divide the dough in two.
Roll and shape each piece of dough into an 8-inch log.
Pour coarse sugar onto a large plate. One at a time, roll the logs in the sugar until the exterior is fully coated.
Tightly wrap the logs in plastic wrap and chill in the refrigerator for at least 4 hours and up to 5 days.
Preheat oven to 350°F (177°C). Line two large baking sheets with parchment paper or silicone baking mats.
Remove logs from the refrigerator. Slice each log into 12 equally thick cookies and place cookies on baking sheets about 2 inches apart.
Bake the cookies for 14–16 minutes, or until set and lightly browned around the edges.
Allow to cool for 5 minutes on the baking sheet, then transfer to cooling rack to cool completely.
