In a small saucepan, melt the butter over medium-low heat, stirring occasionally until it browns. Be careful not to let it burn.
Allow the browned butter to cool for about 10 minutes in the fridge.
In the bowl of a stand mixer, cream together the cooled brown butter, sugar, and brown sugar until smooth.
Mix in the sourdough starter, eggs, and vanilla until combined.
Add the baking soda, baking powder, salt, and flour, mixing until thoroughly combined and scraping the sides often.
Fold in the chocolate chips until evenly distributed throughout the dough.
Transfer the cookie dough to a strip of plastic wrap and roll into a log, covering it completely. Chill the dough in the fridge for 12-24 hours to allow the flavors to develop.
Preheat the oven to 375 degrees Fahrenheit and line baking sheets with parchment paper.
Using a small ice cream scoop, divide the dough into ping pong ball-sized portions, flatten into discs, and sprinkle with flaky sea salt if desired.
Bake for 10-12 minutes or until the edges are golden brown and the center is no longer shiny. Allow to cool before serving.