In a non-reactive metal, or glass bowl, whisk the egg yolks and sugar until thick and lemon colored. Combine the cream and milk in a non-reactive saucepan and heat to the scalding point (when bubbles form around the edge of the pan). Gradually add about 1/2 of the cream to the egg mixture, whisking constantly. Add the egg yolk, sugar and cream mixture to the saucepan with the cream and milk, and cook over low heat until the mixture thickens slightly. Be careful not over cook or boil, as the custard will curdle.
Remove the custard from the heat, add the chocolate and vanilla, and stir until the chocolate is melted. Strain the custard through a fine mesh sieve into a cold bowl. Cover with plastic wrap, pressing it down on the surface to prevent a skin from forming. Refrigerate for at least 2 hours, or until thoroughly chilled.
Pour the custard into the bowl of an ice cream maker, and churn according to the manufacturerís suggested instructions. (Use a 3 or 4-quart ice cream maker, or churn the ice cream in batches.) Place frozen ice cream in a freezer-safe container and freeze overnight until firm.