Preheat oven to 350 degrees F. Butter the bottom and sides of a 8-inch square baking pan. Put a long piece of parchment paper in the bottom of the pan, letting the parchment extend up two sides of the pan and overhang slightly on both ends. Place another piece of parchment paper in the same manner, perpendicular to the first sheet. (This will make it easy to remove the bars from the pan after they have baked.) Butter the parchment.
In medium heatproof bowl set over a pan of almost-simmering water, melt chocolates and butter, stirring occasionally until mixture is smooth. Whisk in cocoa and espresso until smooth. Set aside to cool slightly.
In a medium bowl, whisk together eggs, sugar, vanilla, and salt until combined, about 15 seconds. Whisk warm chocolate mixture into egg mixture; then stir in flour with wooden spoon until just combined. Pour mixture into prepared pan, spread into corners, and level surface with rubber spatula; bake until slightly puffed and toothpick inserted in center comes out with a small amount of sticky crumbs clinging to it, 35 to 40 minutes. Cool on wire rack to room temperature, about 2 hours.
Using parchment overhang, lift brownies from pan. Cut into 1-inch squares and serve. Brownies can be wrapped in plastic and refrigerated up to 5 days.