Preheat the oven to 160°C fan (180°C conventional). Line a 9 x 9 inch square tin with baking paper.
In a heatproof bowl, melt the butter and chocolate together over a bain-marie or in the microwave. Stir until smooth, then set aside to cool slightly until just warm.
In a separate bowl, sift together the flour and cocoa powder. Give it a quick stir and set aside.
Crack the eggs into a large mixing bowl, add the sugar, and whisk with an electric hand mixer until the mixture looks pale and a little frothy.
Pour the cooled chocolate-butter mixture into the eggs and sugar. Use a spatula to gently fold them together until fully combined.
Add the flour and cocoa mixture, folding it through until no dry patches remain.
Stir in the chocolate chips, distributing them evenly through the batter.
Spread the brownie mixture evenly into the prepared tin and smooth the top.
Bake for 35–40 minutes. The brownies should wobble slightly when they come out of the oven but will set as they cool.
Leave to cool completely in the tin before slicing. They’ll firm up even more once cut.