Preheat the oven to 350F and line 2 baking sheets with parchment paper.
Make the Cookie Dough
Brown the butter on medium-low heat until brown flecks appear. Remove from heat and allow the browned butter to cool for 5 minutes
In a medium bowl, whisk together the dry ingredients - flour, salt, and baking soda. Set aside.
In a large bowl or bowl of a stand mixer, whisk/mix browned butter and sugar together for 2 minutes at medium speed. Add the egg yolks, sourdough starter, and vanilla and mix well.
Add the dry ingredients to the wet ingredients and mix.
Spoon the dough onto parchment paper lined baking sheets and use the back of a spoon to flatten it to 1/4” thick circles, or roll the dough into balls and flatten it before baking.
Bake at 350F in the preheated oven for 10 minutes or until the edges are golden brown. After baking, while the cookies are still on the baking sheet, lightly dust them with powdered sugar.
Set the cookies on a cooling rack to cool before serving.