Heat the oven to 350°F. Line a rimmed 18×13-inch sheet pan with parchment, leaving overhang on the long sides for lifting. Lightly grease any exposed metal. For thicker brownies, fold a double layer of foil to form a 1-inch dam along one long and one short edge to slightly reduce the baking area.
Whisk the dry ingredients: In a medium bowl, whisk together the flour, cocoa, espresso powder, and fine sea salt until evenly combined; set aside.
Melt the chocolate and butter: Place the butter and bittersweet chocolate in a heatproof bowl set over a pan of barely simmering water. Stir until smooth and fully melted, then remove from heat and stir in the vanilla. Keep warm to the touch.
Beat eggs with sugars: In a large bowl, whisk the eggs, granulated sugar, and brown sugar for 1 to 2 minutes until slightly thickened and the mixture looks glossy (no need to whip to a ribbon). Tip: For an extra shiny, crinkly top, set the bowl over warm—not hot—water while whisking to help dissolve the sugars.
Emulsify: While whisking constantly, slowly stream the warm chocolate mixture into the egg-sugar mixture until smooth and uniform.
Fold in the dry ingredients in two additions with a spatula just until no dry streaks remain. Fold in about two-thirds of the chopped dark chocolate; do not overmix.
Rest the batter for 10 minutes to thicken and hydrate the cocoa. Scrape the batter into the prepared pan, smooth the top, and tap the pan firmly on the counter 2 to 3 times to release air bubbles. Sprinkle the remaining chopped chocolate over the surface.
Bake for 18 to 22 minutes, rotating the pan once at 12 minutes, until the edges are set, the center is slightly soft, and a toothpick comes out with a few moist crumbs (not wet batter).
Cool on a rack for at least 20 minutes. Sprinkle a pinch of flaky sea salt over the warm brownies if using, lift out using the parchment overhang, and cut into 24 squares.