Heat the oven to 375ºF with a rack in the center. Spray an 8×8-inch metal square cake pan with nonstick cooking spray, then line with parchment, leaving an overhang on all four sides.

Place the butter in a small saucepan or skillet over medium heat. Melt the butter until it starts to foam and sputter, 2-4 minutes. Whisking often, continue to cook the butter until it starts to quiet down, smells nutty, and turns deeply golden brown, another 3-5 minutes. Remove from the heat and immediately pour into a large heatsafe bowl.

Immediately whisk the cocoa and vanilla into the warm brown butter until smooth. Whisk the sugar and salt into the brown butter mixture until combined. Beat in the eggs one at a time, whisking vigorously to combine, about 1 minute. Fold in the starter discard until combined, then fold in 59 grams (2 ounces, about 6 tablespoons) of the chopped chocolate.

Pour the batter into the prepared pan and smooth as needed to make an even layer. Sprinkle over the remaining chopped chocolate. Bake until a tester inserted into the center comes out with some moist crumbs, 29 to 32 minutes. Immediately sprinkle the surface with flaky salt, then let cool for at least 35 minutes, ideally 1 hour.

Lift the brownies out of the pan by the parchment and place on a cutting board. Cut into pieces. Brownies will keep in an airtight container at room temperature for up to 5 days, in the fridge for up to 10 days, or in the freezer for up to 4 months.