Cream butter, brown sugar, and white sugar in a stand mixer. Add in the egg, vanilla extract, and sourdough starter. Mix until incorporated.
Add the peanut butter and mix until just incorporated. Do not overmix.
Next, add the flour, baking soda, and salt, and mix until incorporated.
Chill the cookie dough in the fridge for at least one hour, but up to 24 hours to allow the dough to ferment.
Preheat the oven to 350 degrees. When the oven is preheated, scoop out the cookie dough using a 2 ounce scoop or about 4 tablespoons each. Place the cookie dough 2 inches apart on a baking sheet lined with parchment paper or a Silpat.
Flatten the cookies with a fork in a criss-cross pattern or with the bottom of a glass cup.
Return the remaining cookie dough to the fridge.
Bake the cookies at 350 degrees for 12 minutes, until the center is set and the edges are turning a light golden brown.
Allow cookies to cool completely before transferring them off of the baking sheet. Store in an airtight container. This recipe makes about 20 cookies.