Soak the gelatine in cold water. Grate the zest of the lemon.
Bring the cream, sugar, lemon zest and 1 packet of vanilla sugar to the boil. Add half of the basil and let it steep for about 20 minutes. Drain the mixture through a sieve. Squeeze out the gelatine well and dissolve it in the still warm mixture. Let the cream cool down a little.
Roughly chop the remaining basil, add to the cream mixture and finely puree with the puree. Pour the mixture into four glasses and chill for at least 5 hours.
Mix the strawberries with 1 packet of vanilla sugar, puree and spread on the panna cotta.