In a medium saucepan, combine the heavy cream, whole milk, and half of the sugar. Heat the mixture over medium heat, stirring occasionally, until it begins to steam. Be careful not to let it boil.

In a separate bowl, whisk together the egg yolks, remaining sugar, and salt until the mixture turns pale and slightly thickened.

Once the cream mixture is steaming, gradually pour a small amount into the egg yolk mixture while whisking constantly to temper the eggs. Continue to gradually add the hot cream mixture, whisking continuously.

Pour the entire mixture back into the saucepan and place it over medium-low heat. Cook, stirring constantly with a wooden spoon, until the custard thickens and coats the back of the spoon, about 5-7 minutes. Do not let it boil!

Remove from heat, then stir in the vanilla extract and chopped chocolate until melted and smooth.

Strain the custard through a fine-mesh sieve into a clean bowl to remove lumps. Cover with plastic wrap pressed directly onto the surface of the custard to prevent a skin from forming. Chill in the refrigerator for at least 4 hours, or overnight.

Once the custard is chilled, churn it in an ice cream maker according to manufacturer’s instructions until it reaches a soft-serve consistency, usually about 20-25 minutes.

Transfer churned ice cream to a freezer-safe container and freeze for an additional 2-3 hours, or until firm.

Serve the chocolate custard ice cream scooped into bowls or cones.