Preheat the oven to gas 6, 200 C, fan 180 C, and line 2 baking sheets with nonstick baking paper. Melt the dark chocolate in a heatproof bowl set over a pan of simmering water, until smooth. Set aside to cool slightly.
In a mixing bowl, beat the butter and sugars with a wooden spoon or an electric hand whisk, until pale and creamy. Gradually beat in the eggs, one at a time, then whisk in the cooled melted chocolate.
In a separate bowl, mix the flour, baking powder and cocoa with a pinch of salt, then sift over the cookie mix. Fold in gently, along with the white chocolate and 80 g milk chocolate.
Use 2 spoons to divide the mixture equally into 18 large golf-ball sized pieces and place on the baking sheets 4 cm apart.
Bake for 15 mins, or until firm but still soft in the centre. Remove from the oven and leave to cool for 5 mins, then transfer to a wire rack to cool a little more.
Meanwhile, melt the remaining milk chocolate in a heatproof bowl set over a pan of simmering water. Drizzle over the cookies with a teaspoon. Leave to set, then serve warm or cold.