In the bowl of a stand mixer fitted with the paddle attachment, or using a handheld mixer, beat the butter and sugar together on medium-high speed until light and fluffy.
Add the egg yolks and vanilla extract and beat on medium speed until combined, scraping down the bottom and sides of the bowl if necessary.
Add the flour and salt and beat on low-medium speed until a dough forms. The dough will be thick. Form the dough into a log and wrap it in cling wrap and refrigerate the dough for one hour.
Once the dough has chilled for an hour, preheat your oven to 350 degrees and line a baking sheet with parchment paper.
Unwrap the dough and place it on a lightly floured surface. Roll the dough out until it is about ¼ inch thick. Use a cookie cutter to cut out the cookies, placing them on the baking sheet about an inch apart. They will not spread much. Repeat this process with the remaining dough.
To ensure the cookies really keep their shape while baking, pop the cookie sheet with the cookies on it in the freezer for 10-15 minutes prior to baking.
Bake for 9-11 minutes or until lightly golden. Remove from the oven and let them cool for 5 minutes on the pan, then transfer them to a cooling rack to cool compltely.