I found this recipe on the cooking blog One Perfect Bite. If you don't wish to make your own applesauce, a quart of store-bought unsweetened applesauce can be used. Cake needs to chill overnight before serving.
Preheat oven to 350 degrees F. Fit a 9-inch circle of waxed or parchment paper into a greased and floured 9-inch springform pan. Grease and flour paper. Set aside.
Combine flour, baking powder and cornstarch in a small bowl. Whisk to combine.
In a medium bowl, beat egg yolks with water. Add 1/3 cup of sugar and the vanilla and beat with an electric mixer until frothy and lemon colored.
In a separate small bowl, beat egg whites with remaining sugar until stiff but not dry. Fold into yolk mixture. Stir flour mixture into egg mixture. Scrape into prepared pan. Bake for 20 minutes, or until cake tester inserted into center of cake comes out clean. Transfer to a rack to cool.
If using fresh apples, place apple chunks into a 3-quart saucepan and cook until very soft. Mash. If using prepared applesauce, place into saucepan and warm. Add sugar, rum or vanilla extract and lemon zest. Cook until mixture mounds in a spoon.
Soften gelatin in cold water. Place into a pan of simmering water and stir to dissolve. Stir gelatin into applesauce. Set aside to cool. Applesauce will thicken quickly in refrigerator.
Combine almonds, 1 tablespoon sugar and butter in a nonstick frying pan. Cook over medium heat, stirring, until almonds turn a golden brown. Transfer to paper toweling to cool.
Soften gelatin in milk. Place in pan of simmering water and stir to dissolve. Cool.
Whip cream with remaining 2 tablespoons sugar until it begins to thicken. Add gelatin and continue beating until soft peaks form.
Remove cake from pan; split horizontally into two layers. Brush each layer with 2 tablespoons rum. Transfer one layer to a cake plate. Mound applesauce on top of layer. Cover with remaining layer and pat down to evenly distribute applesauce.
Generously frost top and sides of cake with whipped cream. If desired reserve some cream for decorating top of cake.
Pat almonds around sides and sprinkle on top of cake. Refrigerate overnight before serving.