Preheat oven to 350 degrees. Line baking sheets with Silpat baking mats or parchment paper. Set aside.
In the bowl of an electric mixer fitted with the paddle attachment, combine butter and sugar. Beat on medium until light and fluffy, about 2 minutes. Add vanilla, lemon zest, and salt. Beat to combine. Add egg yolks, 1 at a time, beating well after each addition, until fully combined. Reduce speed to low, and add flour, 1 cup at a time, beating until fully combined
Roll a walnut-size piece of dough into a ball, then roll out into a rope about 3 inches long and 1/4 inch in diameter. Shape into a decorative S. Transfer to prepared baking sheet. Repeat with remaining dough, placing cookies about 1 1/2 inches apart on baking sheet. Bake until firm, 12 to 15 minutes. Transfer to wire racks to cool.
The cookies will keep in an airtight container for up to 2 weeks.