- In a saucepan off the heat, whisk together the sugar and cornstarch. Whisk in the egg yolks until smooth. Whisk in the cream and milk.
- Cook over medium heat, stirring constantly with a wooden spoon, scraping the sides and bottom of the pan, until the mixture begins to simmer, thickens and coats the back of the spoon, about 15 minutes. Remove from the heat.
- Add the chocolate. Stir until the chocolate has melted and the mixture is smooth. Pour into a bowl. Cover with plastic wrap directly on the surface of the mixture and let cool. Refrigerate for 4 hours. If desired, place the bowl over an ice bath for faster chilling (see note). Strain the mixture through a sieve.
- Pour the chilled mixture into the ice cream maker and churn for 30 minutes or until the ice cream has set.
- Transfer to an airtight container and freeze for 1 hour or until firm. Let the ice cream sit at room temperature for several minutes before serving, if needed.
The mixture can be made in advance and refrigerated for up to 4 days before being churned.