In the bowl of an electric mixer fitted with the paddle attachment, beat butter and salt at medium speed until pale and fluffy, about 1 minute. Add powdered sugar and beat until smooth, 1-2 minutes. Beat in vanilla and melted chocolate until combined. Add Nutella and heavy cream, and beat until combined and frosting is smooth and fluffy. Add more powdered sugar if needed, until frosting is spreadable.
Use immediately or store in the fridge, covered, for up to 3 days. Before using, bring to room temperature and whisk until smooth.