Sift the flour, cocoa powder and baking powder into a mixing bowl. Add the sugar and stir together.
Add the melted butter, beaten eggs, milk and vanilla and fork together until almost mixed. Stir in the chopped white chocolate.
Spoon into paper cake cases arranged in a 12-hole deep muffin tin and bake in a preheated oven, 200°C (400°F), Gas Mark 6, for 18–20 minutes until well risen. Leave to cool in the tin for 5 minutes then transfer to a wire rack.
Melt the plain dark or milk chocolate in a heatproof bowl set over a saucepan of gently simmering water, then drizzle the chocolate in random lines over the top of each muffin.
Serve the muffins warm or cold. They are best eaten on the day they are made.