Preheat your oven to 350°F. Line an 8x8-inch baking pan with parchment paper leaving a 2-inch overhang along each side.
Combine chocolate and butter in a saucepan over very low heat and stir constantly until melted and smooth, or melt in the microwave at 50% power in short bursts with frequent stirring.
Combine eggs and both sugars in a large bowl and whisk vigorously until pale and thick. This will take a minute or two. You could also use an electric mixer, but I like using a whisk by hand. Mix in salt and vanilla.
Add warm melted chocolate mixture and mix it in until well incorporated. The batter should tighten up and look glossy once it is evenly blended.
Combine flour, cocoa powder and espresso powder in a small bowl and whisk well to remove any lump. Sprinkle it over the surface of the chocolate batter and fold it in until evenly combined. Fold in chocolate chips. Spread the batter evenly into prepared pan and bake for 20-24 minutes.