Cream the butter and 1/2 cup of the sugar together with an electric mixer on medium speed until smooth and fluffy, scraping down the sides of the bowl as necessary. Add the egg yolks one at a time, beating after each addition. Scrape down the sides of the bowl. Beat for 1 minute and add the vanilla.

Combine 1 1/4 cups of the flour and the salt in a small mixing bowl and add to the butter mixture. Mix on low speed until fully incorporated. Increase the speed to medium and mix until the dough is thick and creamy, about 2 minutes.

Generously dust a large sheet of parchment or waxed paper with the remaining 2 tablespoons flour. Spoon the dough down the center of the paper, fold the paper tightly over the dough, and roll into a cylinder about 2 inches in diameter and about 17 inches long. Refrigerate for 4 hours.

Preheat the oven to 350°F. Line 2 large baking sheets with parchment paper.

Remove the dough from the refrigerator and peel away the paper. Using a sharp knife, cut the dough into 1/4-inch-thick slices. Place them on the baking sheet about 1 1/2 inches apart. Sprinkle with 1 tablespoon of the remaining sugar. Bake until lightly golden, 13 to 15 minutes. Remove the cookies from the oven and let cool completely on the sheet. Remove them from the sheet using a spatula or thin knife. Repeat the process with the remaining dough and sugar.