Pour 1 cup of the cream into a medium saucepan and add the sugar and salt. Scrape the seeds from the vanilla bean into the saucepan and add the pod to the pot. Warm over medium heat, stirring, until the sugar is dissolved.
Remove from the heat and add the remaining 2 cups cream (or the remaining 1 cup cream and the milk) and the vanilla extract.
Chill the mixture thoroughly in the refrigerator. When ready to churn, remove the vanilla bean, rinsing and reserving it for another use, and then freeze the mixture in your ice cream maker according to the manufacturer's instructions.