Preheat the oven to 325°F. Grease a 9x13 baking dish or line it with parchment paper.
Melt the butter and pour it into a large mixing bowl.
In a separate bowl, whisk together the flour, cocoa powder, salt, and baking soda.
Add the sugar, sourdough starter, egg, egg yolk, and vanilla to the melted butter. Whisk until smooth and combined.
Add the dry ingredients and shredded zucchini to the wet ingredients. Do not squeeze the moisture out of the zucchini.
Stir until the batter comes together. It will be thick at first, but the zucchini will release moisture as you mix.
Let the batter sit for 10 to 15 minutes, then stir again.
Optional ferment: Cover the bowl and let the batter rest at room temperature for 4 to 6 hours, or refrigerate it overnight.
Fold in the chocolate chips, saving a small handful to sprinkle over the top if desired.
Spread the batter into the prepared 9x13 pan. Smooth the top with a spatula and sprinkle with reserved chocolate chips.
Bake for 35 to 42 minutes, or until the edges are set and a toothpick inserted in the center comes out with moist crumbs.
Let the brownies cool completely before slicing. For extra fudgy brownies, chill before cutting.