Prepare the Berry Sauce recipe and set aside to cool a bit. Whisk together the cream, milk, sugar, salt, and vanilla. Add 1/3 cup of the Berry Sauce and stir to combine. Place the remaining berry sauce in the refrigerator to chill while the ice cream is churning.
Pour into your ice cream maker and freeze according to the manufacturer's instructions. Scoop the churned ice cream into a freezer container, adding a few spoonfuls of the COLD berry sauce along with the ice cream. Swirl lightly with a knife and freeze until firm.