Add your sticks of butter to a skillet and heat over medium/low heat. Stir constantly as it simmers until it becomes golden in color and has some browned bits on the bottom of the pan. Mine took about 15 minutes but if you use a larger skillet it could be less so just use your eyes not the clock on this.
Once the butter is brown remove it from the heat and set aside. In a large mixing bowl add in the brown sugar, coconut sugar, salt, and baking soda. Stir until combined. Pour the browned butter into the sugar mixture and stir until well combined.
Add in the eggs, sourdough starter, and vanilla extract. Stir until combined and then add in your flour. Stir until flour is almost all incorporated into the sugar and then add in your chocolate chips. Stir until evenly distributed. Cover the bowl with plastic wrap and refrigerate for at least 8 hours and up to 24.
After the dough has rested and chilled scoop out cookie dough in 2 Tablespoon worth balls and place on a cookie sheet lined with parchment paper or greased with butter.
Bake the cookies in a 325F oven for about 20 minutes or until the edges are golden brown and the centers are just barely set. Let sit on the cookie sheet for 5 minutes and then remove to a wire rack to cool. Store in an airtight container at room temp for up to 5 days.