Peel, dice and mash the mango, saving all the juice. Chill.
Combine buttermilk, whole milk, heavy cream and sugar until well incorporated and sugar is dissolved. Split vanilla bean lengthwise and scrape seeds into milk mixture. Add split pod. Mix well. Refrigerate 1 hour.
Remove vanilla bean pod and discard. Pour milk mixture into canister of an ice cream freezer. Churn according to manufacturer’s instruction about 10 minutes. Slowly add chilled mashed mango and its juices and continue churning 15 minutes. Scrape into a bowl, cover and place in freezer 1 to 2 hours. To serve, scoop into bowls and garnish with pistachios and basil.