Beat cream and vanilla together on high speed until soft peaks are achieved. Fold in half the condensed milk then fold in the other half making sure the mixture is thoroughly combined.
Melt the Sunbutter either in the microwave for 1-2 minutes or on top of the stove – it does not need to be runny, just very soft. Let cool then fold into the cream mixture 3-4 times, leaving ribbons of the SunButter running throughout.
Spoon half the mixture into a 9 by 5 loaf pan.
Put 1 cup of the strawberry preserves into a small bowl and stir vigorously to loosen it up. Dollop half the preserves on top of the SunButter mixture. Using a spoon, swirl the preserves into the SunButter mixture. Top with the remaining SunButter mixture, dollop on the rest of the loosened preserves on top and swirl again. Cover with plastic wrap and freeze for 4 hours or until completely frozen. Can be made several days or even a week ahead. Let the ice cream sit at room temperature a few minutes before serving.
Before serving, combine the strawberries with the rest of the strawberry preserves in a small saucepan. Heat over medium heat until the preserves have melted. Stir to coat all the strawberries.
Scoop the ice cream into serving dishes and top with the chunky strawberry sauce.