Combine the sugar, milk, salt and cocoa in a saucepan over medium heat. Stir constantly and bring to a simmer. Place egg yolks into a small bowl and gradually stir in about ½ cup of the hot liquid.
Return the liquid to the saucepan and heat until thickened. Do not let the liquid boil. Remove from heat and stir in the chopped semisweet chocolate until it melts. Pour the liquid into a chilled bowl and refrigerate for two hours until cold, stirring occasionally. When the mixture has cooled completely, stir in cream and vanilla. Pour into your ice cream maker and freeze according to the manufacturer’s directions.