Preheat oven to 350 degrees and position rack in center of oven.
Grease bottom only of cake pans with butter and flour/cake spray and for added measure, line bottom of pans with parchment paper.
Combine flour with salt in a small bowl and set aside.
In a standing mixer, whip the egg whites on medium-low speed until foamy and then add the cream of tartar and continue mixing until the whites become opaque.
Add ½ cup sugar slowly to the side of the bowl and increase the speed of the mixer until soft but not stiff peaks form. Scrape the contents to another bowl and set aside.
Using the same bowl, add the egg yolks and whip at high speed for 3 to 5 minutes until lightened in color.
Slowly add the remaining sugar, cold water, and vanilla into the egg yolks and mix until combined on low speed.
Sift the flour onto the egg yolks in two additions, and stir gently with a large spatula to combine.
Gently but thoroughly fold in the whipped egg whites.
Transfer mixture to prepared pans and bake for about 20 to 30 minutes until cooked through.
Remove from oven, cool for about 10 minutes in the pans and then carefully remove the cakes from the pan.
After fully cooled, wrap and refrigerate or freeze.
In a small bowl, add egg yolks and cornstarch. Whisk to blend and set aside.
In a medium saucepan, add milk, sugar, salt, and vanilla or chocolate. Heat until small bubbles form and remove from heat.
Temper eggs by adding small amounts of the hot milk mixture while whisking quickly to prevent the eggs from curdling.
Return everything to the saucepan and cook over medium heat and stir constantly until thickened.
Cool the pastry cream and refrigerate until ready to use.
When ready to assemble the cake, whip heavy cream until soft peaks form and then fold together with cooled pastry cream.
Add gelatin and water to a small saucepan and heat gently just until the gelatin dissolves.
Whip the cream and sugar until slightly thickened, then add the gelatin mixture slowly and continue whipping until firm.
Combine all ingredients for the rum syrup in a saucepan and heat until sugar dissolves.
Using a teaspoon or small squeeze bottle, distribute the rum syrup evenly over each of the three cake layers.
Place one cake layer on the bottom of a cake board or cake dish, soak with rum syrup, and spread vanilla pastry cream on top.
Add another layer of sponge cake, soak with rum syrup, and spread chocolate pastry cream on top.
Top with final layer of sponge cake, frost the cake, and add crushed peanuts or sliced almonds to the sides.
Decorate the top if desired and refrigerate until serving.
