Beat the eggs well and set aside. Measure out the cocoa and set aside.
Combine sugar, cornstarch and salt in a large saucepan. I use our medium sized stock pot. Gradually stir in all of the half-and-half. Cook over medium heat until mixture begins to simmer, stirring constantly.
Gradually stir about 1 cup of the hot mixture into the beaten eggs. Add egg mixture to the remaining hot mixture, stirring constantly. Cook and stir over low heat until slightly thickened (about 2 minutes).
Stir in the cocoa, beating with a whisk until smooth. Add the vanilla and mix well. The mixture will be about the consistency of a thin pudding.
Don't worry about mixing in the remaining heavy cream yet. Refrigerate the mixture as long as you can.
Ideally, the mixture will chill overnight, but we have taken it from stovetop to ice cream maker and while it takes longer to set, and takes more ice, it still turns out fine.
Once the cream mixture is cool, follow these instructions for using the ice cream maker.
When you get to the step of adding the cream mixture to the cream can, you will add both the chocolate mixture and the heavy whipping cream.
The dasher will mix it all together so don't worry about mixing in the cream ahead of time.