Combine whipping cream, condensed milk and vanilla in a large bowl or the bowl of your stand mixer. Whip together until medium peaks form. Add in the chopped chocolate and gently fold it in until evenly distributed.
You can use your favorite caramel recipe or store-bought caramel. If using rum, pour it into the caramel and mix together until fully combined.
Add half of your ice cream mixture into a freezer-safe container. Drizzle half of the caramel over top and using a knife, swirl it through the ice cream. Pour the other half of the ice cream mixture over top and drizzle the remaining caramel over top. Again, use a knife to swirl it through the ice cream.
Place in the freezer for at least 6 hours until firm. Remove from the freezer for about 10 minutes so that it softens enough to scoop.