In a large saucepan, whisk together the milk, cream and cocoa powder. Bring the mixture to a simmer over med-low heat and then turn the heat off. Stir in the chocolate and vanilla until the chocolate has melted.

Add 3/4 cup of the sugar to the milk mixture and bring to a simmer, whisking occasionally to dissolve the sugar.

In a medium bowl, whisk the remaining sugar and egg yolks until the mixture is slightly thickened and light in color. Slowly, add 1/4 cup of the milk mixture to the eggs while whisking constantly. Continue adding the milk to the egg mixture 1/4 cup at a time until all the ingredients are combined.

Prepare an ice bath in a large bowl and place a medium bowl in the ice bath. Place a fine mesh stainer over the bowl.

Transfer the cream mixture to a large saucepan and cook over medium heat, stirring constantly and scraping the bottom and sides with a heatproof spatula until the custard thickens enough to coat the back of a spoon. Strain the custard into the bowl and allow to cool.

Refrigerate the custard until cold or overnight.

Pour the custard into the freezer can of an electric ice cream maker and freeze according to the manufacturer's instructions. When the ice cream is the consistency of soft serve. Transfer to an airtight storage container and freeze.