Preheat oven to 150 C / Gas 2. Line 4 - 20x30cm or similar sized tins with baking parchment.
In a large glass or metal mixing bowl, beat egg whites until foamy. Sprinkle with cream of tartar. Gradually add 400g caster sugar, continuing to beat until stiff peaks form. Fold in 250g cashew nuts. Divide meringue between the 4 tins and spread evenly to edges.
Bake in preheated oven for 30 minutes or until light golden brown. Remove the meringue from the baking tins while still hot; allow to cool. When cool, trim edges so that all 4 meringue layers are uniformly shaped. Set aside.
To make buttercream filling: In a large bowl, beat butter until light and fluffy. In a separate large bowl, whip egg yolks until thick and lemon coloured.
Meanwhile, in a saucepan, combine 400g sugar and 250ml water. Bring to the boil and heat to 132 to 143 degrees C or until a small amount of syrup dropped into cold water forms hard but pliable threads. Add the hot syrup in a thin stream to the beaten egg yolks, while beating at high speed. Beat in the whipped butter until smooth. Beat in rum.
On one layer of meringue, spread approximately 1/4 of the buttercream evenly to edges. Repeat layers until all is used. Smooth sides with spatula. Sprinkle top with 250g chopped cashews. Freeze until solid. To serve, cut 2.5cm slices from the frozen dessert.
Almonds or hazelnuts can be used in this recipe instead of cashews.
The buttercream can be flavoured with any flavour of liqueur, coffee powder or fruit jam.