Toast hazelnuts and remove skins by rubbing in a kitchen towel.

Finely chop the hazelnuts in a food processor or blender and set aside.

In a saucepan, warm milk, 1 cup of heavy cream, sugar, and salt.

Remove from heat, add chopped hazelnuts, cover, and steep at room temperature for 1 hour.

Place finely chopped milk chocolate in a large bowl.

Heat the remaining 1 cup of cream in a saucepan until just boiling.

Pour hot cream over the milk chocolate and stir until smooth and melted.

Set a mesh strainer over the chocolate mixture.

Strain the hazelnut-infused milk into a medium saucepan, squeezing the nuts to extract liquid; discard nuts.

Rewarm the hazelnut-infused mixture.

Whisk egg yolks in a separate bowl.

Slowly pour the warm hazelnut mixture into the egg yolks, whisking constantly.

Scrape the warmed egg yolk mixture back into the saucepan.

Stir constantly over medium heat until the mixture thickens and coats the spatula.

Pour the custard through the strainer into the melted chocolate mixture.

Add vanilla extract and stir until cool over an ice bath.

Chill the mixture thoroughly in the refrigerator.

Freeze in an ice cream maker according to manufacturer's directions.