Whisk the egg yolks in a large nonreactive saucepan; set aside. Warm the milk and cream in a small saucepan over medium heat, stirring often to keep the mixture from scorching, for about 5 minutes, until it has begun to steam. Add the mixture to the yolks in a slow, steady stream, whisking continuously.
Set the saucepan over medium heat, add the vanilla, sugar, and salt, and stir for about 2 minutes, until the sugar has dissolved. Continue cooking, stirring continuously, for another 5 minutes, or until the mixture begins to thicken; do not allow to boil. Transfer the pan to an ice bath to stop the cooking and stir until the steaming stops.
Transfer the mixture to an airtight container, cover, and refrigerate for at least 6 hours, or overnight.
Freeze the mixture in an ice cream maker according to the manufacturer’s instructions. When it is finished, transfer the ice cream to an airtight container and freeze overnight to harden. The ice cream can be stored in the freezer for up to 5 days.