Break off a quarter of the white chocolate. Using a potato peeler, shave off some chocolate curls to decorate the desserts.
Place the remaining pieces of chocolate in a small heatproof bowl. Add the milk and microwave on full power for 2 minutes. Leave to stand for 1 minute then stir. If lumps remain in the chocolate, microwave again for a further 30 seconds until melted. (Alternatively, put the chocolate and milk in a small heatproof bowl and rest it over a small saucepan of gently simmering water.) Stir in the cream and pour into a cool bowl, allow to cool completely, then put in the freezer for 5 minutes.
Reserve 4 blackberries and blend the remainder in a food processor with the honey until puréed. Turn into a fine-meshed sieve over a bowl and press the purée through with the back of a dessertspoon to extract the seeds.
Whisk the egg white until it stands in soft peaks when the whisk is lifted from the bowl.
Remove the chocolate cream from the freezer and whisk until it starts to thicken. This might take a few minutes. Gently stir in the egg white.
Spoon half the chocolate mixture into 4 small serving dishes or cups and spoon over the fruit purée. Top with the remaining chocolate mixture and give each a light stir with the handle end of a teaspoon so you can see a swirl of the blackberry purée. Decorate with the reserved berries and chocolate curls and chill until ready to serve.