Combine the milk, cream, cocoa powder, vanilla, and salt in a heavy saucepan over medium heat until steaming with small bubbles around edges.
In a separate bowl, whisk the egg yolks and sugar vigorously for 2 minutes until pale and thick.
Slowly pour 1 cup of the hot milk mixture into the egg mixture while whisking constantly to temper the yolks.
Pour the tempered yolk mixture back into the saucepan with the remaining milk mixture.
Cook over low heat, stirring constantly with a wooden spoon until the custard thickens and coats the back of the spoon, about 6-10 minutes.
Strain the hot custard through a fine-mesh strainer into a clean bowl.
Add the Nutella to the hot custard and whisk until completely melted and uniform in color.
Press plastic wrap directly onto the surface of the custard and refrigerate for at least 8 hours or overnight.
Pour the cold custard into an ice cream maker and churn according to manufacturer's instructions until it reaches thick soft-serve consistency.
Transfer the gelato to an airtight container and freeze for at least 2 hours until firm.