Brown the Butter: In a light-colored saucepan over medium heat, melt the 2 sticks of butter. Swirl pan occasionally as it foams and sizzles. After 5-7 minutes, foaming will subside and brown specks with a toasted nutty aroma will form at the bottom. Immediately remove from heat.
Melt Chocolate & Bloom Cocoa: Immediately add 4 oz of the chopped dark chocolate and Dutch cocoa powder into the hot brown butter. Stir until smoothly melted and glossy. Let cool slightly.
Whip Eggs for Crinkle Top (The Secret): In a large mixing bowl with an electric hand mixer or stand mixer whisk attachment, beat eggs, egg yolk, granulated sugar, and brown sugar on high speed for a full 5 to 7 minutes. The mixture must become very pale, thick, and fall in ribbons. This dissolved sugar-protein foam creates the shiny paper-thin crackly crust.
Combine Liquids: Gently stream the lukewarm chocolate brown butter mixture and vanilla extract into the whipped eggs on low speed until combined.
Fold Dry Ingredients: Sift in all-purpose flour, fine sea salt, and espresso powder. Use a rubber spatula to gently fold just until flour streaks disappear. Fold in remaining 4 oz chopped chocolate chunks.
Pan & Bake: Pour thick glossy batter into an 8x8-inch or 9x9-inch baking pan lined with parchment paper with overhang. Smooth the top. Bake at 350°F (175°C) for 28 to 32 minutes until edges are set and a toothpick inserted in the center comes out with moist, fudgy crumbs (never raw wet batter).
Salt & Chill: Sprinkle generously with Maldon flaky sea salt immediately upon leaving the oven. Cool completely in the pan for 2 hours, then refrigerate for 30 minutes for ultra-clean bakery slice edges.