Preheat oven to 400°F (200°C). Line a 9-inch springform pan with parchment and grease the sides.

Beat egg yolks, warm water, and sugar for base until pale and fluffy. Mix in vanilla extract.

Combine cake flour and baking powder. Fold into yolk mixture until smooth.

Beat egg whites and salt until stiff peaks form. Fold into batter gently.

Pour batter into pan and bake for about 15 minutes until a toothpick comes out clean.

Cool sponge cake, peel off parchment, and let cool on a rack.

Whip heavy cream to stiff peaks and refrigerate.

Sprinkle gelatin over cold water and set aside.

Beat yogurt, sugar, and lemon juice until sugar is dissolved.

Dissolve gelatin over simmering water, temper with yogurt mixture, and mix gelatin mixture fully into yogurt.

Fold chilled whipped cream into yogurt mixture.

Slice sponge cake into 2 layers. Add bottom layer into the springform pan, fill with cream mixture, and top with the second layer. Chill for at least 4 hours.