For the ice cream, put the egg yolks and sugar in a bowl and whisk together until combined. Put the milk and cream in a pan and bring to the boil. Pour over the egg yolks and whisk well. Pour back into the pan and return to the heat. Warm until it thickens.
Put the white chocolate in a large heatproof bowl. Pour the custard mixture through a sieve onto the white chocolate and stir well until the chocolate has melted. Allow the mixture to cool, then pour into an ice cream machine to churn. Place in a freezer-proof container and freeze until solid.
Preheat the oven to 180C/160C Fan/Gas 4 and line a baking tray.
Put the pears, lemon zest and juice, sugar, vanilla pod and seeds into a pan. Add enough water to just cover the pears. Bring the mixture to the boil, then simmer until the pear is tender (5 -15 minutes). Remove the pears and drain on kitchen paper until cool. Slice into strips and dust with icing sugar.
For the brandy snap basket, melt the sugar, golden syrup and butter in a saucepan, remove the pan from the heat. Add the flour and ground ginger and mix to form a thick paste. Pour onto a work surface lined with cling film. Roll the mixture into a ball, then cover in the cling film and chill in the fridge for 30 minutes, or until set.
Remove from the fridge and roll out walnut-sized balls of dough, you should get at least four. Dust a work surface with flour. Roll each ball of dough into a disc about 2mm thick. Place on the baking tray. Bake for 6-8 minutes, or until crisp and golden-brown. Set aside to cool for about 1 minute.
Carefully lift each brandy snap off the tray and rest over an upturned glass. Press the overhanging edges down gently against the sides. Leave to cool for a couple of minutes, then lift off the glass and set aside to cool completely.
Place the brandy snap basket in the centre of a plate and put a spoonful of ice cream in the basket. Place the pears around the basket along with the mint and white currants.