In a large bowl, combine the softened butter and sugars. (Make sure the butter is soft enough to mix with the sugar by hand.)
Add the egg to the mixture, stirring until incorporated.
Stir in the sourdough starter and vanilla extract.
Add the flour, salt, and baking soda, careful to not overmix.
Finally, incorporate the chocolate chips and let the dough refrigerate for 15 minutes or refrigerate up to overnight. (I have made them without refrigeration and they get more cake-like in texture.)
When ready to bake the cookies, preheat the oven to 350°F. (Let the refrigerated cookies come to room temperature.)
Drop spoonfuls (2-3 tablespoons) of dough onto a parchment-lined baking sheet. (I use a 3 tablespoon ice cream scoop.) Bake 8-10 minutes for a cake-like cookie. Bake 6-8 minutes for a chewier cookie. (My recommendation!) The cookie MAY appear a little wet in the center and that is ok. It will continue to bake and be cooked throughout after being out of the oven for a few minutes.