Put cream and milk into a medium saucepan over medium-high heat. Heat the mixture until hot (do not let simmer), about 2 minutes. Remove from heat; cover, and let stand 30 minutes.
Prepare an ice-water bath; set aside. Put egg yolks, sugar, and salt into the bowl of an electric mixer fitted with the whisk attachment. Beat on high speed until mixture has tripled in volume and can hold a ribbon on surface for 2 seconds, about 3 minutes.
Reduce speed to medium. Ladle 1 cup cream mixture in a slow stream into yolk mixture to temper it. Add another cup cream mixture; beat to combine. Transfer to pan with the cream mixture; cook over medium-high heat, stirring constantly, until it is thick enough to coat the back of a wooden spoon and mixture registers 180 degrees.on an instant-read thermometer, 5 to 7 minutes. Stir in melted chocolates.
Pour custard through a medium-mesh sieve into a bowl set in ice-water bath. Let cool completely, stirring often.
Freeze custard in an ice cream maker according to manufacturer's instructions. Use immediately, or freeze in an airtight plastic container until ready to serve. If frozen more than 4 hours, let stand at room temperature 20 minutes before serving.
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