In the bowl of a stand mixer fitted with a paddle attachment, cream the butter, sugar, and salt, beating until light and fluffy.
Beat in the egg yolks, then the vanilla extract.
Add the flour gradually with the mixer on low, beating until well incorporated.
Divide the dough into 4 sections and roll each out into a 6- or 7-inch log. Wrap with plastic wrap and refrigerate for 2 hours.
When ready to bake, preheat oven to 350 degrees Fahrenheit and line your cookie sheets with parchment paper. Set aside.
Remove 1 log from the fridge and cut into quarter-inch slices. Place on cookie sheet at least 1 inch apart and bake for 12-14 minutes, or until golden brown.
Let sit on cookie sheet for 5 minutes before removing to a wire rack to cool completely.
Repeat with the remaining logs until it is all baked.
You can also freeze the logs for up to 2 months, thawing in the refrigerator before slicing and baking.