Line an 800ml pudding basin with cling film. Put the ice cream in a food processor and quickly whizz until soft. Stir through 150g of the Christmas cake, crumbed into pieces, and the brandy and then transfer to the pudding basin. Cover the surface with more cling film and then freeze until required.
Slice the rest of the Christmas cake. Take a loose-bottomed cake tin, which is just wider than the pudding basin and line the base with the Christmas cake slices, cutting to fit and pressing down gently so the cake sticks together as a round. Remove the cake tin but keep the cake on the base. Remove the ice cream from the pudding basin and place it on top of the sponge with the wider base at the bottom. Return to the freezer while you make the meringue.
For the meringue, put the sugars and the water in a small saucepan and the egg whites into the bowl of a freestanding mixer. Stir the sugar over a gentle heat until it dissolves, then leave it to come to the boil, using a sugar thermometer to keep an eye on the temperature. When the sugar reaches 114°C start whisking the eggs whites. When it reaches 120°C, remove from the heat and slowly pour into the egg whites. Whisk until completely cold (around 10 minutes).
Working quickly, remove the ice cream from the freezer and cover the entire dome with meringue, peaking it to create a nice shape and making sure there are no holes. Once covered, return the Alaska to the freezer for around an hour.
When you’re ready to serve, preheat the oven to 220°C/200°C fan/gas mark 7. Bake for 3-4 minutes until the meringue sets and is golden brown. Serve immediately.