Whisk in your milk, cocoa powder, and chocolate hazelnut spread into a saucepan over medium heat. Bring the milk to a simmer and then remove from the heat. Do not boil.
Add your heavy cream and vanilla extract to your mix, stir to combine. Cover your bowl with plastic wrap, making sure to have the plastic wrap touching the surface of the ice cream base so it does not get a skin. Refrigerate for at least 3 hours.
Press plastic wrap the surface of the ice cream. Freeze for at least 4 hours, or until solid. To serve, allow ice cream to sit at room temperature for at least 5 minutes. Scoop and enjoy!