Line a 36cm x 25cm tin with baking parchment. First make the roulade. Break the chocolate into pieces and melt in a bain-marie (that is, in a heatproof bowl over a pan of simmering water).
Place the butter and sugar in a bowl and whisk until creamy and fluffy using an electric whisk. Add the eggs and continue to beat – the mixture will split but this is normal. Pour in the melted chocolate and mix well. Add the Kahlua and milk, and mix until smooth. Fold in the flour, then place the mixture in the prepared tin and spread it out evenly.
To make the filling, whisk the cream until it stands in very soft peaks using an electric whisk. Lightly mix in the grated chocolate and vanilla. Take care not to overwhip the cream or it will lose its light, soft texture. Place the cooled roulade on the work surface, baking-parchment side down, and spread the filling on top, keeping a space clear all around the edge.
Use the parchment paper to help you roll up the roulade into a log. Wrap the paper around the roulade and shape it with your hands into a smooth log, allow to sit for 5 minutes, then transfer on to a serving plate, removing the paper. Top with dark and white chocolate shavings.