Finely chop fresh basil and combine with granulated sugar and lemon zest. Let it sit for 10-15 minutes.

In a medium saucepan, combine heavy cream, whole milk, and a pinch of salt. Heat until it reaches a gentle simmer.

Slowly pour the herb mixture into the cream mixture while stirring constantly. Cool to room temperature.

Cover and chill in the refrigerator for at least 2 hours.

Pour chilled mixture into an ice cream maker and churn for 20-30 minutes until thick.

Transfer to an airtight container and freeze for at least 4 hours before serving.