Step 1: Preheat your oven to 350°F (175°C) and line an 8×8 inch square baking pan with parchment paper, leaving an overhang on the sides for easy removal.
Step 2: In a medium saucepan, melt the butter over medium heat. Continue cooking, stirring constantly, until it browns and smells nutty. Remove from heat immediately.
Step 3: Whisk the white miso paste into the hot browned butter until completely smooth and integrated.
Step 4: Add the chopped dark chocolate to the butter mixture and let it sit for a minute, then stir until the chocolate is fully melted and the mixture is glossy.
Step 5: In a separate large bowl, whisk together the granulated sugar, brown sugar, and eggs for about 2-3 minutes until the mixture is pale and slightly thickened. Stir in the vanilla extract.
Step 6: Slowly pour the chocolate-miso-butter mixture into the egg mixture, whisking constantly to combine without scrambling the eggs.
Step 7: Sift the flour and cocoa powder over the wet ingredients. Use a rubber spatula to gently fold the dry ingredients in until no streaks of flour remain.
Step 8: Pour the batter into the prepared pan and smooth the top. Bake for 22-25 minutes. The center should still have a slight wobble, and a toothpick should come out with a few moist crumbs.
Step 9: Allow the miso brownies to cool completely in the pan before lifting them out and slicing into 16 squares.