Puree the raspberries, juice and sugar in a food processor until smooth. Pour through a mesh strainer into a bowl and discard the raspberry seeds. Stir in the buttermilk, cream and a pinch of salt, then cover and refrigerate until cold, about 1 hour.
Transfer the mixture to an ice cream maker and freeze according to the manufacturer's instructions. Transfer to an airtight container and freeze until firm, at least 2 hours. Serve sprinkled with pepper.