Place the butter in a saucepan over medium heat. Begin whisking right away. Stir as it bubbles, and after 3 to 4 minutes or so you should see brown bits appear on the bottom of the pan. Remove from heat immediately and continue to whisk for another 30 seconds. Let the butter sit and come to room temperature – a softened solid. You can do this way before, just be sure the butter if soft.
Preheat the oven to 325 degrees F.
Stir together the flour and salt. In the bowl of an electric mixer, add the butter and sugar and beat on medium speed until fluffy, about 3 minutes. Beat in the egg yolks one at a time and the vanilla bean paste. Slowly add in the dry ingredients until just mixed.
Pat the dough in a 1/2-inch thick round on a floured surface. Use a biscuit cutter to create rounds or form them yourself – as long as they are about 1/2-inch thick. Place the rounds on a baking sheet and bake for 10 to 12 minutes, or until just slightly golden. Let the shortbread cool completely, then crumble it into a bowl.