Brown butter and let it cool completely.
In a large mixing bowl or the bowl of a stand mixer with the paddle attachment, cream butter and sugar on medium speed until fluffy.
Add egg, yolks, and vanilla extract. Mix until smooth. Stir in sourdough starter discard.
In a separate bowl, whisk together dry ingredients: flour, salt, and baking soda.
Add flour mixture to the wet ingredients in stages, mixing on low speed until a soft dough forms.
Scoop cookie dough balls onto a parchment-lined cookie sheet.
Bake at 350°F (175°C) for 9–11 minutes, or until edges are golden brown.
Cool on the baking sheet 2 minutes before transferring to a wire rack.