Preheat the oven to 350F. Butter and line a 9-by-13-inch metal baking dish with parchment paper. Set aside.
In a small saucepan, melt the butter and chocolate over low heat.
In a medium mixing bowl, combine the eggs, sugars, salt, and vanilla. Whisk until the mixture thickens, becomes pale in colour and reaches a creamy consistency.
Add the flour, cocoa powder, and espresso powder into the egg mixture and fold it in quickly but gently with the rubber spatula so that you don’t deflate the air that’s been incorporated into the eggs.
Using a rubber spatula, fold the cooled chocolate into the egg mixture.
Pour the batter into the prepared dish and smooth the top with a spatula.
Bake until the top looks slightly cracked and feels soft to the touch, about 25 minutes.