Preheat the oven to 180°C (350°F/Gas 4). Line two baking trays with baking paper.
Sift the flour and cocoa powder into a large bowl, add the brown sugar and make a well in the centre.
Combine the butter and dark chocolate in a small heatproof bowl. Half-fill a saucepan with water and bring to the boil. Remove the pan from the heat. Sit the bowl over the saucepan of water, making sure the base of the bowl does not touch the water. Stir occasionally until the chocolate and butter have melted and are smooth. Mix well.
Add the butter and chocolate mixture and the egg to the dry ingredients. Stir with a wooden spoon until well combined, but do not overmix. Stir in the chocolate chips.
Drop tablespoons of the mixture onto the prepared trays, allowing room for spreading. Bake for 7–10 minutes, or until firm to the touch. Cool on the trays for 5 minutes, then transfer to a wire rack to cool completely. Store in an airtight container.