In a large bowl, combine egg nog, heavy whipping cream, sweetened condensed milk, rum and vanilla. Mix well and refrigerate until chilled. Pour into an ice cream maker and churn for 45-50 minutes, or according to manufacturer’s instructions.
When finished churning, pour a quarter of the ice cream into a freezable container. Spoon about a third of the Nutella over the top in random globs. Repeat with remaining ice cream and Nutella, finishing with the top layer of ice cream. Cover and place in freezer for 4 hours, or until completely firm. Serve with chopped hazelnuts, if desired.