Preheat the oven to 350°F and line 2 baking sheets with parchment paper.
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 flour, salt, and baking soda. Set aside.
In a large bowl, whisk/mix browned butter and sugar together for 2 minutes. Add the egg yolks, sourdough starter, vanilla, lemon juice, and lemon zest and mix well.
Add the dry ingredients to the large bowl and mix together. Stir in the chopped white chocolate chips.
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 350°F 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 wire rack to cool before serving.