For the ice cream, make a custard base. In a pan, bring the milk and cream up to the boil. In a bowl, whisk together the egg yolks and sugar until pale. Pour the milk and cream over the yolk mixture and whisk together. Place back into a pan and cook over a low heat (to reach 82C/180F on a cooking thermometer) until the custard is thick enough to coat the back of a spoon.
Add the glycerine, if using, to help prevent ice crystals forming during freezing. Pour the hot custard over the crumbled Christmas pudding and stir to mix. Pour the mixture into an ice cream maker, churn according to manufacturer's instructions and freeze.
For the cake, put the unpeeled oranges in a pan with a lid. Cover with cold water, bring to the boil and simmer for 1½-2 hours, or until the skins are soft and the insides broken down.
Drain and, when cool enough to handle, cut each orange in half and remove the seeds. Chop everything finely — skins, pith, fruit — in the food processor.
Preheat the oven to 160C/325F/Gas 3 and grease and line a 24cm/9½in loaf tin or a 20cm/8in cake tin.
Weigh the orange pulp and keep 450g/1lb (discard the rest). Place back in food processor with all the dry ingredients and add the eggs one at a time until you have a smooth batter.
Pour the cake mixture into the prepared tin and bake for 1 hour -1 hour 20 minutes, or until the sides start to come away from the tin. Check the cake after 40 minutes and cover with aluminium foil to stop the top burning.
Remove the cake from the oven and leave to cool on a wire rack. When the cake is cold, remove it from the tin.
For the sauce, add all the ingredients to a saucepan and place over a low heat until simmering. Continue to cook until the plums are very soft and almost a purée.
Remove the cinnamon stick. Blend the spiced plums in a blender until smooth. Pass through a fine sieve into a bowl and set aside until needed. If you find the purée too thick, add a little water.
Serve the cake in slices with a scoop of ice cream and a drizzle of sauce.
Make things easier for yourself by preparing the oranges a few days in advance and buying vanilla or clotted cream ice cream instead of making your own. Simply let it soften for 30 minutes in a cool room before mixing in the Christmas pudding and returning it to the freezer.