Place butter in a saucepan over medium heat. Melt the butter while frequently stirring. The butter will start to foam and bubble. After a few minutes, it will go from pale yellow to brown with a sweet caramel scent. Remove from the heat and let cool.
Once cool, beat the butter and sugar together for several minutes. Add the egg yolks and mix well. Add the vanilla and the sourdough starter. Mix until well incorporated.
In a seperate bowl, mix the flour, baking soda, and salt. Add it to the wet mixture and gently stir until just combined. Fold in the chocolate chips. Don't overmix. Refrigerate for 1 hour, and up to 3 days for a long ferment.
Scoop into balls and place on a lined cookie sheet. Bake at 325° for 11-15 minutes. Don't overbake. Cool on the tray for 5 minutes* and move to a cooling rack to finish cooling.