In a medium bowl, whisk together the flour and salt.
Using an electric mixer, beat the butter, granulated sugar, lemon zest, and vanilla on medium speed until fluffy, 2 to 3 minutes. Reduce speed to low and gradually add the flour mixture, mixing until just combined (do not overmix).
On a piece of parchment, form the dough into a rectangular block, 12 by 2 by 1 inches (use a ruler or metal spatula to square off the sides). Wrap in the parchment and refrigerate until firm, about 3 to 4 hours.
Heat oven to 350°F Cut the dough into â…“ inch-thick slices and place on baking sheets spaced 1 inch apart; sprinkle with the coarse sugar.
Bake, rotating the baking sheets halfway through, until the edges begin to brown, 12 to 15 minutes. Cool slightly on the baking sheets, then transfer to wire racks to cool completely. Store the cookies in an airtight container at room temperature for up to 7 days.