Melt the butter on a stove till it's just browning, then remove it so it doesn't burn.
Add the brandy and set aside to cool.
Warm the milk in a pan, while you whisk the yolk and sugar till it is lighter in colour. Don't let the milk boil.
On the stove
Pour the hot milk over the sugar mixture, whisking continuously, then return to the saucepan set over a low heat. Cook for 3-4 mins, stirring the whole time until the custard thickens enough to coat the back of the spoon.
In the Thermomix
If you've whisked the sugar mixture in the Thermomix, add the hot milk to the sugar mixture and cook on 60C/3:30mins/speed1. This should make a custard, thick enough to coat the spoon.
Once all the sauces are cooled:
Whisk the double cream to stiff peaks. Mix the brandy butter with the custard then mix in to the cream. Make sure it's all combined well, then put it in the freezer.
Making the ice cream
If you have an ice cream maker, follow the instructions to make ice cream. If you don't, add it to your Thermomserver or any other dish and remove from the freezer every half hour to stir and break down all the crystals.
After 5 times - about 2.5 hours - crumble the Christmas pudding into the ice cream mix together, and leave to set till you're ready to serve. (If you're using an ice cream maker, follow their instructions on adding bits.)
Remove 10 - 15 minutes before serving, depending on your outside temperature, and enjoy.
Recipe by Keeper of the Kitchen at https://www.keeperofthekitchen.com/2015/08/03/brandy-butter-christmas-cake-icecream/