Brown the butter on medium-low heat in a small saucepan.  Once the butter is golden brown, remove it from heat and allow it to cool a little bit, then pour it into a large bowl or the bowl of a stand mixer.

Add the sugars to the large bowl with the brown butter and mix.  Adding the sugars to the butter before adding the egg yolks prevents them from scrambling when coming into contact with the hot/warm butter.  

Once the butter and sugar are combined, add the egg yolks, sourdough starter, and vanilla and mix until combined.

Whisk the dry ingredients (all-purpose flour, salt, baking powder, and baking soda) together in a separate bowl, and then add the dry ingredients to the large bowl of wet ingredients and mix until just combined.  Do not overmix.

Add the chopped pecans (optional) and rough-chopped chocolate chips and stir.

Use a cookie scoop or spoon the cookie dough onto a parchment-lined baking sheet and bake at 350F until you have crispy edges but the middles are still soft, 10-12 minutes.

Place the cookies on a wire rack to cool.