Prepare an ice-water bath. Whisk together yolks, salt, and 1/2 cup sugar in a medium bowl.
Bring cream, milk, and remaining 1/2 cup sugar to a simmer in a medium saucepan over medium-high heat. Immediately remove from heat. Ladle 1 cup cream mixture into yolk mixture, whisking constantly. Whisk in another 1 cup cream mixture until well combined. Transfer yolk-cream mixture to the saucepan.
Cook over medium-high heat, stirring constantly, until mixture is thick enough to coat the back of a spoon and registers 180 degrees on an instant-read thermometer, 5 to 7 minutes. Stir in melted chocolate.
Transfer to a large bowl, and set over ice-water bath. Let cool completely, stirring frequently. Strain through a fine sieve, and churn in an ice cream maker according to manufacturer's instructions.