In a large bowl with an electric handheld mixer (or in the bowl of a stand mixer), mix the butter and sugar until fluffy and combined.
Add the egg yolks and vanilla and mix until combined, scraping the bowl to mix it thoroughly.
Add the flour and salt and mix until it comes together. Once it forms pea-size crumbs, use your clean hands to form the dough into a ball.
Shape the soft dough into small balls- about 3 teaspoons worth of dough. Place the balls close together on a parchment-lined baking sheet.
Press a small indentation with your thumb in each cookie ball – don’t make it too wide. If the sides crack, just press them together.
Preheat the oven to 375 degrees F. Space the cookies about an inch or so apart on two large parchment-lined baking sheets. They’ll puff and spread just slightly but not very much. Bake for only 10 to 11 minutes until set and just lightly browned on the edges.
(The centers may get puffy while baking, just gently press them back down after they come out of the oven.) Allow the cookies cool completely.