Preheat your oven to 350°F. Line a 9x9-inch baking pan with parchment paper, leaving an overhang on two sides to use as handles for lifting the brownies out later.
In a medium saucepan over low heat, melt the butter. Add the chocolate chips, cocoa powder, and vanilla extract. Stir constantly until the chocolate is fully melted and the mixture is smooth and glossy. Remove from heat and let cool for 5–10 minutes.
In a large bowl using a stand mixer or hand mixer, beat the eggs, egg yolk, granulated sugar, and dark brown sugar together on medium-high speed for 7–10 minutes. The mixture should be pale, thick, and fall from the beaters in a thick ribbon — this builds the signature crinkle top.
Add the sourdough discard and the cooled chocolate mixture to the egg mixture. Mix on low speed until just combined — do not overmix at this stage.
Add the flour and salt. Using a rubber spatula, fold them in by hand until just combined. Stop as soon as you no longer see dry streaks of flour. Overmixing will make the brownies cakey rather than fudgy.
Pour the batter into the prepared pan and use a spatula to spread it into an even layer.
Bake for 35–40 minutes, until the top is set and a toothpick inserted in the center comes out with a few moist crumbs (not wet batter). The edges should be set and pulling away slightly from the sides of the pan. Do not overbake — the brownies will continue to set as they cool.
Let the brownies cool completely in the pan before lifting them out using the parchment overhang. Slice into 9 squares with a sharp knife, wiping the blade clean between cuts for the cleanest edges.