Grease a 9x13-inch (23x33-cm) dark metal pan with softened butter, then line with parchment paper, leaving overhang on all sides. Grease the parchment with softened butter.
Combine the chopped chocolate, ¼ cup (30 g) of cocoa powder, and espresso powder in a heatproof liquid measuring cup or medium bowl and set aside.
Add the butter to a small saucepan over medium heat and cook until the butter just comes to a vigorous simmer, about 5 minutes, swirling the pan occasionally. Immediately pour the hot butter over the chocolate mixture and let sit for 2 minutes. Whisk until the chocolate is completely smooth and melted, then set aside.
Combine the granulated sugar, brown sugar, vanilla extract, salt, and eggs in a large bowl. Beat with an electric hand mixer on high speed until light and fluffy, about 10 minutes. It will be similar to the texture of very thick pancake batter.
With the mixer on, pour in the slightly cooled chocolate and butter mixture and blend until smooth.
Position a rack in the middle of the oven and preheat to 350°F (180°C).
Sift in the flour and remaining cocoa powder and use a rubber spatula to gently fold until just combined.
Pour the batter into the prepared baking pan and smooth the top with a spatula. Bake until lightly puffed on top, about 20 minutes.
Remove the baking pan from the oven using oven mitts or kitchen towels, then lightly drop the pan on a flat surface 1-2 times until the brownies deflate slightly. Sprinkle with flaky sea salt.
Return the pan to the oven and bake until a wooden skewer inserted into the center of the brownies comes out fudgy but the edges look cooked through, about 20 minutes more. The center of the brownies will seem under-baked, but the brownies will continue to set as they cool.
Set the brownies on a cooling rack and cool completely in the pan.
Use the parchment paper to lift the cooled brownies out of the pan. Cut into 24 bars and serve immediately.