Prepare the tin. Preheat the oven to 160°C fan (325°F). Line a 23cm (9-inch) square metal baking tin with nonstick baking paper.
Melt the chocolate and butter. Place the butter and dark chocolate in a heatproof bowl set over a pan of gently simmering water and stir until smooth. Alternatively, microwave on medium power in 30-second intervals, stirring between each one. Set aside to cool until barely warm.
Whisk the eggs and sugar. Add the eggs and caster sugar to a large mixing bowl. Using an electric hand whisk or stand mixer fitted with the whisk attachment, whisk on high until very pale, thick and increased considerably in volume. The mixture should fall from the whisk in a thick ribbon that briefly sits on the surface.
Add the chocolate. Pour the barely warm chocolate and butter mixture into the whipped eggs and sugar. Gently fold together until evenly incorporated, taking care not to knock out too much of the air.
Add the dry ingredients. Sift the flour and cocoa powder into the chocolate mixture and gently fold until just combined. Stop as soon as no dry streaks remain.
Bake. Pour the batter into the prepared tin and spread it evenly. Bake for 10 minutes, rotate the tin, then bake for another 6–8 minutes. The top should look shiny and crackled and the edges should be set, while the centre remains slightly soft.
Cool. Remove from the oven and leave the brownies to cool completely in the tin for at least 1 hour before slicing into 16 squares.