Line an 800ml pudding basin with cling film. Put the ice cream in a food processor and quickly whizz until soft. Stir through the brandy and 150g fruit cake, crumbed into pieces. Transfer to the pudding basin. Cover the surface with more cling film, then freeze until required.
Slice the rest of the fruit 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.
Put the sugars and 60ml 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 egg whites. When it reaches 120°C, remove from the heat and slowly pour into the egg whites. Whisk for 10 minutes until completely cold.
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 an hour. When you’re ready to serve, preheat the oven to 220°C/fan 200°C/gas mark 7. Bake for 3-4 minutes until the meringue sets and is golden brown. Serve immediately.