In a large saucepan combine undrained jackfruit and 1/3 cup sugar. Bring to a boil, reduce heat and simmer, uncovered , about 30 minutes or until soft. Remove from heat and cool slightly. Transfer jackfruit mixture to a blender and blend until smooth. Cool completely.
In a large bowl combine cream, coconut milk, remaining 1/3 cup sugar, and salt. Stir in half of the jackfruit puree. Cover and chill overnight.
Freeze ice cream mixture in a 2-quart ice cream freezer according to manufacturer's directions. Transfer to a freezer container and swirl in remaining jackfruit puree. Cover and freeze at least 4 hours before serving. Serve with sliced, ripe jackfruit and roasted cashews, if desired.