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Lightly grease an 8" square pan, then line with parchment and lightly grease the parchment. Preheat the oven to 350°F with a rack in the center.
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In a large saucepan, heat the butter, granulated sugar, and brown sugar over medium heat, stirring occasionally to encourage even melting, until the mixture is very hot (the butter should be bubbling around the edges of the pan) and the sugar is starting to dissolve, 3 to 5 minutes.
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Remove the pan from the heat and immediately whisk in the cocoa, vanilla, and salt, whisking until the mixture is smooth. Let cool for 5 minutes (the mixture and pot should still be quite warm), then add the eggs one at a time, whisking vigorously after each addition. The mixture may look greasy and broken after the first egg, but it will turn smooth and glossy after the second.
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Whisk in the sourdough starter and baking powder until no streaks of starter remain, then vigorously stir in 1/2 cup (85g) chocolate chips, encouraging them to melt into the warm batter.
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Pour the batter into the prepared pan and sprinkle with the remaining 3 tablespoons (32g) chocolate chips.
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Bake the brownies for 22 to 26 minutes, until the top is shiny but not wet-looking, the edges are starting to pull away from the sides of the pan, and an inserted toothpick comes out with no raw batter.
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Let the brownies cool completely in the pan, about 1 hour. For the easiest slicing, cover the cooled brownies and chill in the refrigerator for at least 1 hour.
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Brownies keep best (and taste best!) wrapped tightly and stored in the refrigerator, where they'll last for up to 1 week, or the freezer, where they’ll last for several months. Serve cold or at room temperature.
