Prepare the Pan: Preheat the oven to 350°F (175°C), using a conventional oven rather than a fan-assisted setting. Grease an 8×8-inch metal baking pan, then line the bottom and two sides with parchment paper, leaving about 1 inch of overhang on the sides for easy removal. Combine Cocoa Mixture: Place the Dutch-process cocoa powder, 4 ounces of chocolate, and espresso powder in a medium bowl. Set the bowl aside while you prepare the butter.
Brown the Butter: Melt the butter in a light-colored saucepan over medium-low heat. Once it becomes foamy, continue cooking while frequently swirling the pan to keep the butter moving. White milk solids will begin appearing on the bottom. Keep swirling and cooking until those solids turn brown, the butter becomes golden, and it develops a nutty aroma. Combine Butter Chocolate: Immediately remove the browned butter from the heat and pour it over the cocoa and chocolate mixture. Stir until the chocolate has melted and the mixture is smooth. Set aside to cool.
Whip the Egg Mixture: In a stand mixer fitted with the paddle attachment, or in a large bowl using an electric beater, combine the white sugar, brown sugar, vanilla, and eggs. Beat on medium-high speed for about 3 minutes, until the mixture is thick, smooth, and noticeably lighter in color. Add the Chocolate Mixture: Reduce the mixer speed to low and slowly pour the cooled chocolate mixture into the egg mixture. Continue mixing just until the chocolate is fully incorporated.
Finish the Batter: Keeping the mixer on low speed, add the flour and salt. Mix only until incorporated, then fold in the additional chocolate chips. The finished batter will be very thick.
Fill the Pan: Transfer the thick brownie batter to the prepared pan. Use a spoon or spatula to spread it evenly across the pan.
Bake the Brownies: Bake for 22–24 minutes, watching carefully after the 20-minute mark. The surface should look glossy and just set, rather than jiggly in the center. Small cracks may appear. Avoid overbaking, as the brownies continue cooking and develop more cracks while cooling. Cool Before Cutting: Leave the brownies in the pan for at least 30 minutes before lifting them out using the parchment overhang. Cut the cooled brownies into squares and finish with coarse salt flakes such as Fleur de Sel or Maldon's.