Preheat oven to 300 degrees F (150 degrees C). Line 4 - 8x12 inch pans with parchment paper.
In a large glass or metal mixing bowl, beat egg whites until foamy. Sprinkle with cream of tartar. Gradually add 2 cups white sugar, continuing to beat until stiff peaks form. Fold in 2 cups chopped nuts. Divide meringue between the 4 pans, and spread evenly to edges.
Bake in preheated oven for 30 minutes, or until light golden brown. Remove the meringue from the baking pans 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 colored.
Meanwhile, in a saucepan, combine 2 cups sugar and 1 cup water. Bring to a boil, and heat to 270 to 290 degrees F (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 2 cups chopped cashews. Freeze until solid. To serve, cut 1 inch slices from the frozen dessert.