Start by making the sponges, pre-heat your oven to 160C. Lightly grease two 7inch round cake tins with butter or spray oil. Line the base and sides with greaseproof paper. Break up both chocolates into separate bowls and melt in the microwave in 30-second blasts, stirring in-between, until smooth. Set aside. In a small bowl, mix the cocoa powder, espresso powder and boiling water together to make a chocolatey paste. Set aside. In a large bowl, cream the butter, sugar and vanilla together until light and fluffy. Beat in the eggs one at a time until well combined. Now fold in the flour and milk to make a smooth cake mixture.
Divide the mixture evenly between two bowls. Fold the melted white chocolate into one bowl. Fold the melted milk chocolate and chocolatey paste into the other bowl. Spoon the cake mixtures into the baking tins, smoothing out the tops. Bake for 35-40 minutes until risen and springy to the touch. Leave to cool completely.
To make the butter creams, break up both chocolates into separate bowls and melt in the microwave in 30-second blasts, stirring in-between, until smooth. Set aside for now. Beat the butter until soft and lump-free. Sift in the icing sugar in stages and beat until well combined and smooth. Divide evenly between two bowls. Mix the melted white chocolate and 2 tbsp milk into one bowl. Mix the melted milk chocolate and 2 tbsp milk into the other bowl.
To assemble the cakes, use a sharp flat knife to slice each cake into two layers. This should give you 2 white chocolate sponges and 2 milk chocolate sponges.Sandwich the sponges together using the white chocolate buttercream (saving roughly a third of the buttercream for the rope border), alternating the sponges between white, milk, white, milk.
Coat the outside and top of the cake using the milk chocolate buttercream (again saving roughly a third of the buttercream for the rope border). Place the fridge for at least 1 hour to chill and firm up (this is important for the ganache drip).Meanwhile spoon the leftover buttercream into a large piping bag fitted with a large open star piping nozzle. Set aside for now.
To make the ganache drip, very finely chop the dark chocolate and place in a microwave-safe bowl. Pour the cream on top of the chocolate. Microwave in 10-20 second blasts, stirring in-between each, until the chocolate starts to melt and the cream is piping hot but not boiling. Once you reach this stage, keep stirring the mixture until the ganache is smooth and glossy. Leave to cool for 5 minutes, until the ganache reaches the perfect 'drip' consistency (check out the blog post above for more help with this).Pour the ganache into a piping bag and snip off the very end. If you don't have a piping bag, you can instead do the drip with a spoon.Take the chilled cake out of the fridge and pipe the ganache around the outside edge of the cake, applying more pressure for longer drips and less pressure for shorter drips.
Use the leftover ganache to fill in the top of the cake, smoothing it out with a palette knife. Leave the ganache to set for 30 minutes.
Start by piping a dot of buttercream on top of the cake. Then turn your piping bag on a 45° angle and pipe the buttercream in a circular motion moving around the outside edge of the cake. Slice the cake into 12 and serve straightaway. If you have leftovers, store the cake in an airtight container, at room temperature, and eat within 3-4 days.