Trace a 9 inch circle on 2 sheets of parchment paper. Set aside for later use.
In a bowl combine wheat flour with 1/3 cup sugar. Then add the chopped hazel nuts and mix to combine.
In the bowl of a stand mixer, beat the egg whites on high speed until foamy,
Add the cream of tartar and beat until soft peaks begin to form. Add the sugar and vanilla and beat until stiff peaks form.
Gently fold in the hazel nut and flour mixture into the egg whites.
Dab 5 dots of the meringue onto each baking sheet. Lay the prepared parchment paper on top (traced side down). This will help hold the parchment in place.
Split the hazelnut meringue amongst the 2 (9 inch) circles. Try to spread within the lines as bet as possible. Bake at 300 degrees Fahrenheit for 10 minutes then drop the temperature to 220 degrees Fahrenheit, bake for another 3 hours and 45 minutes.
Let the meringue cool completely. Place a 9 inch round pan on top and cut around the edges. Do this to both cakes. Reserve the outside edge that's been cut; you will need it to coat the sides of the finished cake.
In a bowl lightly beat 2 eggs with 1 1/4 cup sugar.
In a sauce pan, bring the milk to a simmer (not a boil). Slowly pour it into the eggs and sugar making sure to stir constantly.
Pour the egg and milk mixture back into the saucepan and continue stirring over medium low heat until it becomes yellow and thickened. This may take up to 10-15 minutes.
Remove the saucepan from heat and add the vanilla extract. Stir to combine. Let it cool to room temperature.
Beat the room temperature butter in a stand mixer using the whisk attachment.
Pour in the cooled egg mixture while continuing to mix. Then add the rum.
Reserve 1 1/2 cups of the butter cream. Combine it with 1/4 cup cocoa powder.
Spread the white buttercream on top of the first meringue layer. Don't use up all of the white butter cream; reserve about 1/3 cup for decorating.
Place the second meringue layer on top of the buttercream. Then spread enough buttercream to thinly coat the sides of the cake.
Spread the chocolate buttercream on the top portion of the cake.
Coat the sides of the cake with the left over meringue crumbles. From here, decorate the cake as you wish.