Separate the egg whites and egg yolks. Add the egg whites and xylitol to a bowl and whisk them well until the mixture becomes foamy.
Mix yogurt, yolks, vanilla, baking powder, lemon zest, and flour in a different bowl. Slowly incorporate the whisked egg whites.
Pour the batter into a round cooking pan covered with a baking sheet.
Add water to a baking tray and put your pan on the tray. This step is optional but will positively impact the baking result. The cake will have a soft sponge-like texture.
Bake it in the middle of the oven at 180° Celsius for about 30–40 minutes. To prevent the cake from getting brown on top, after 20 minutes or so, cover it with a baking paper sheet.
When the cake is completely baked, let it sit for 5 minutes, and then carefully remove it with the baking paper from the pan.
Let it cool down completely. You can serve it plain, with some fruit, or with cashew cream (link to the recipe for peach cashew cream).