In a medium saucepan, over medium heat the sugar cream and milk, whisk together to dissolve the sugar. Let cool completely and refrigerate until chilled.
Pour the chilled cream mixture into your ice cream maker and process according to the manufacturer’s instructions. Towards the last few minutes, toss in the Butterfinger candy pieces. Transfer the ice cream into an airtight container and freeze for a minimum of 4 hours or overnight. Scoop into bowls or into your favorite type of cone to enjoy.