Preheat the oven to 340 degrees Fahrenheit (170 Celsius, or 150 Celsius fan). Grease and line four 8-inch sandwich cake tins with baking paper. Dust with flour and shake out the excess.
Sift the flour, cocoa powder, baking powder, and baking soda into a bowl and set aside.
Bring the chocolate, milk, and dark brown sugar to a boil in a heavy-bottomed pan, stirring occasionally, then remove from the heat.
Beat the butter and caster sugar together on high speed until pale and fluffy. Turn the mixer to low speed and gradually add the beaten eggs until well combined.
Add half the flour mixture and mix until just combined, then add the rest. While the chocolate mixture is still hot, carefully fold it into the batter. Mix until uniform, without overmixing.
Divide the batter evenly between the four prepared tins, filling each about three quarters full. Bake for thirty to forty minutes, turning the tins after twenty minutes so they color evenly.
Cool the sponges on a wire rack, then wrap in plastic wrap and refrigerate.
For the buttercream, place the chocolate in a heatproof bowl. Bring the cream to a boil, pour over the chocolate, let stand for two minutes, then stir briskly until smooth.
Beat the butter and sifted icing sugar on low, then high speed until pale and fluffy. Add the vanilla extract, then pour in the ganache and beat until fully combined.
Trim the tops of the chilled sponges flat. Stack the four layers on a cake board with buttercream between each layer. Press gently to level, then refrigerate for ten minutes.
Trim the sides of the stack flush with the board, then apply a thin crumb coat of buttercream over the top and sides. Refrigerate for ten minutes.
Move the cake to a larger board and apply the remaining buttercream (minus six tablespoons reserved for piping) in an even layer over the top and sides. Smooth with a side scraper held at a forty five degree angle. Chill until ready for the next step.
For the drip, melt the chocolate and butter together in the microwave in ten-second bursts, stirring between each. Stir in the golden syrup, then add sunflower oil until the mixture reaches a drippy consistency.
Let the cake sit at room temperature until cool but not cold. Squeeze the just-warm drip mixture over the rim of the cake to create drips, then pour the remainder over the center and spread to meet the edges. Leave to set.
Brush or spray the chocolate shards with gold luster dust. Pipe six swirls of the reserved buttercream on top of the cake and top each with a gold-dusted chocolate shard.