Soak gelatine in cold water for about 5 minutes. Mix yoghurt, lime juice, sugar and vanilla sugar. Squeeze the gelatine and dissolve at very low heat. First stir 3 tablespoons of yoghurt into the gelatine, then stir everything into the remaining yoghurt.
Chill for 10-15 minutes until the yoghurt begins to gel.
Meanwhile peel 2 persimmons and puree the pulp. Whip the cream until stiff and fold into the yoghurt. Layer yoghurt mousse and kaki puree alternately in four glasses. Pull through spirally with a wooden skewer so that "streaks" form.
Chill for at least 1 hour.
Cut 1 persimmon into slices and place on the mousse.