Add the softened butter and sugars into a large bowl. Your butter should be soft and easy to mix in by hand. If it's not, it'll soften up in about 30 minutes.
Now add the egg. Stir everything together until fully the egg is fully incorporated.
Next, stir in the vanilla extract and the sourdough starter. Then add the salt, baking soda, and flour. (Don't over-mix. You want to do the least amount of mixing necessary to achieve uniform dough. When there are no more streaks of flour in your bowl, go ahead and stop mixing.)
Finally, add the chocolate chips and incorporate into the dough.
The dough needs to refrigerate for at least 15 minutes. The original chocolate chip cookie recipe called for overnight chilling. The longer you let the dough refrigerate, the more firm and thoroughly hydrated your dough will be. (I have tried making them without refrigeration and they get more cake-like in texture if that's what you like.)
Ready to bake? Take the dough out of the fridge and preheat the oven to 350°F. Make sure the dough is at room temperature before baking.
Each cookie is 2-3tablespoons of dough. Portion them onto a baking sheet lined with parchment paper. (I use a 3 tablespoon ice cream scoop.)
My recommended baking time is 6-8 minutes for a chewier cookie. With this recipe, just one or two extra minutes can change the cookies from chewy to cake-like, so bake accordingly.
Now take them out and let them sit for a few minutes. It's normal if the cookies seem to be a tad wet in the center. They will continue to bake after you take them out of the oven and they'll be cooked throughout after a few minutes.