Preheat the oven to 400 degrees F (200 degrees C). Place a large piece of parchment paper over the bottom of a 9-inch springform pan. Make sure it is taught, then clip on the rim and cut off the excess parchment paper. Grease the sides.
Beat egg yolks, warm water and sugar for sponge base in a bowl with an electric mixer until pale and fluffy. Mix in vanilla extract.
Mix cake flour and baking powder together in a separate bowl. Sift over egg yolk mixture and fold in thoroughly until no lumps remain.
Beat egg whites and salt in a glass, metal, or ceramic bowl until stiff peaks form. Fold into the sponge batter using a spatula. Pour into the prepared pan and even out the surface with a spatula or a large knife.
Bake in the preheated oven until a toothpick comes out clean, about 15 minutes. Let cool in the pan for a few minutes, then remove sponge cake from the pan and carefully peel off parchment. Cool on a wire rack.
Whip heavy cream for filling in a bowl with an electric mixer until stiff. Refrigerate.
Pour water into a small heat-proof bowl and sprinkle gelatin over top. Set aside.
Beat Greek yogurt, sugar, and lemon juice in a separate bowl with an electric mixer until sugar is fully dissolved.
Bring a little bit of water to a bowl in small saucepan. Lower the bowl with the gelatin into the water, making sure no boiling water spills into it. Stir until the gelatin is liquid and fully dissolved. Remove the bowl with the gelatin with kitchen tongs.
Add 1 tablespoon of the yogurt mixture immediately to the gelatin and stir until completely incorporated. Add 4 to 5 more tablespoons the same way until the gelatin mix is cooled; it should be smooth and not contain any lumps. Transfer the gelatin mixture into the yogurt mixture and beat with an electric mixer until well blended.
Fold whipped cream into the yogurt mixture until well blended. You may also give it a quick whisk with an electric mixer to blend the two, as long as you don’t overmix.
Grease the sides of the springform pan and place the sponge cake back into it. If the sponge shrunk during baking, push it down gently so it completely fills the pan. Pour the filling into the pan and even it out with a knife or a spatula. Cover with a cake dome (no plastic wrap, it will cling and mess up the surface) and refrigerate until set, at least 4 hours.
Remove cake from the refrigerator. Dip a large knife in cold water and run it all around the filling to loosen. Carefully remove the rim. Dust with confectioners’ sugar just before serving.
The original German recipe is in metric. It is important to use exact measures. If you have a scale, the original metric measures are as follows: 150 gm sugar and 130 gm sifted cake flour for the sponge cake. For the filling use 500 ml heavy cream, 80 ml cold water, 500 gm Greek yogurt, 60 ml lemon juice, and 200 gm sugar.
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