1. Unless using a free-standing sorbetiere or churn, turn the freezing compartment or freezer to the coldest setting about 1 hour before making the pudding.
2. Using a sharp knife, make a small slit in the rounded side of the shell of each chestnut.
3. Bring a saucepan of water to the boil, add the chestnuts and boil for 5 minutes. Drain. Peel the chestnuts while still very hot. Return them to the clean pan and add 125 ml (4 fl oz) of the milk. Simmer gently until the chestnuts are tender, then rub them through a fine sieve into a bowl.
4. Put the egg yolks in a bowl and beat lightly.
5. Pour the rest of the milk into a saucepan and bring to just below boiling point.
6. Pour the milk on to the egg yolks, stirring well. Return the mixture to the clean saucepan and simmer, stirring constantly, until the custard thickens. Do not let it boil.
7. Remove the custard from the heat and stir in the chestnut puree and the sugar. Leave until cool.
8. In a bowl, whip half the cream to soft peaks. Add to the chestnut mixture with a few drops of vanilla essence.
9. Pour into a suitable bowl for freezing, cover and freeze until half frozen (when crystals appear around the edge of the mixture).
10. Meanwhile rinse the cherries, pat dry on absorbent kitchen paper, and chop finely.
11. In a bowl, whip the remaining cream until stiff.
12. Beat the ice cream mixture until smooth, scraping off the crystals.
13. Stir in the chopped cherries and fold in the whipped cream.
14. Return to the freezer until almost set, stirring the mixture frequently.
15. Press into a 750 ml (1 1/4 pint) mould, cover, and return to the freezer until firm.
16. Return the freezer to the normal setting.
17. Transfer the pudding to the refrigerator about 15 minutes before serving, to allow it to soften and "ripen".