Line a 1L bowl with a double layer of clingfilm. Scoop ⅓ of the vanilla ice-cream into the bowl, patting it down well. Top with a layer of crushed cookies. Repeat the process twice and press down firmly to create an even surface. Cover with clingfilm and freeze overnight.
Preheat the oven to 180°C/350°F/Gas 5. Mix all of the cake ingredients. Pour the mixture into a non-stick 18cm tin and bake until golden brown, for about 20 minutes. Let cool completely.
Put the sugar and 100ml of water in a small saucepan and bring to a boil. Cook for about 4 minutes to make a syrup. Meanwhile, whisk the egg whites and the lemon juice until they form soft peaks. Then, gradually and very slowly add the syrup, whisking until the egg whites have cooled down and the meringue is thick and glossy, for 4 to 5 minutes.
Lift the ice-cream out of the bowl and upturn onto the cake. Cut the edge of the cake to fit the ice-cream.
Spread the meringue evenly over the ice-cream and cake, making sure they are completely covered. Using a blow torch, slightly brown the meringue. Slice with a serrated knife and serve straight away.