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Whisk the egg yolks with the sugar and cornflour until thick and pale. Pour the milk into a medium saucepan and bring just to the boil. Gradually whisk into the egg yolk mixture until smooth then return to the pan. Cook over a low heat, stirring until the custard thickens and just coats the back of a wooden spoon. Be careful not to overheat or the custard will curdle.
Stir in the vanilla essence then sprinkle the surface of the custard with a little sugar or add a piece of crumpled and dampened greaseproof paper to stop a skin forming; then leave to cool.
Purée the strawberries in a food processor or liquidiser, in batches if needed, until smooth. Press through a sieve into a bowl, discarding the seeds. Keep to one side.
Whip the cream until it resembles thick batter then mix with the cooled custard. Fold in the strawberry purée. Pour into a freezer-proof container and freeze for 6-7 hours until firm enough to scoop, beating two or three times with a fork to break up the ice crystals.
For the cones; break the white chocolate into pieces and melt in a small bowl set over a small saucepan of gently simmering water. Put the nuts onto a small plate. Dip the tips of four of the cones into the melted chocolate then the nuts. Stand upright in a glass bowl to set. Melt the dark chocolate in the same way then dip the tips of the four remaining cones in the dark chocolate and the nuts and leave to set.
When ready to serve, allow the ice cream to soften at room temperature and scoop into the cones.