In a medium bowl, mix together the flour, baking powder, baking soda, and salt. Set that aside.
In a small saucepan, melt the butter over medium low heat. The butter will melt, get foamy, and start turning golden brown. Once it is golden brown, turn the saucepan off and remove from the heat. This process should take 5 minutes. Allow the butter to cool before adding to the bowl. It should be room temperature before it is mixed into the rest of the ingredients.
Add the room temperature brown butter to a large bowl. Add the brown sugar and granulated sugar. Turn the hand mixer or stand mixer on medium speed and mix for 1 minute until light and fluffy.
Add the sourdough starter, eggs, and vanilla to the bowl. Mix until fully combined.
Carefully add the dry ingredients to the wet ingredients and mix until combined.
Fold in the chocolate chips. Cover the bowl with plastic wrap and refrigerate for at least 30 minutes, up to 24 hours.
Preheat the oven to 375 degrees.
When you are ready to bake the cookies, scoop the dough onto a baking sheet lined with parchment paper or a silicone mat. Bake the cookies for 10-12 minutes or until the edges are just golden brown. Allow the cookies to cool on a wire cooling rack before serving.