In a mixer on low speed, combine the cream cheese and sweetened condensed milk for 20-30 seconds. Increase speed to medium and beat until creamy. Add Greek yogurt and continue beating. Slowly pour heavy cream in as the mixer in going, then add the vanilla extract. Finally, add one tablespoon of Nutella and beat on medium high for a minute or so until combined well.
Transfer mixture to an ice cream maker and churn according to manufacturer's directions. Once churned, transfer to an air-tight container and dot blobs of Nutella on top. Use a butter knife to gently swirl in Nutella. Place plastic wrap flush to the surface of the ice cream and freeze until firm but not rock hard, about 1 hour.
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