Whisk together 2 cups of the half and half with the egg yolks and sugar and cook in the top of a double boiler until thickened, about 5 minutes. Pour half of this mixture into a 4 cup covered container, add the vanilla extract and 1 cup of the heavy cream. Whisk the cocoa into the remaining hot custard mixture, then pour this into a 4 cup covered container along with the remaining 1 cup of heavy cream. Chill the ice cream mixtures completely.
Freeze ice cream, one flavor at a time, in an ice cream machine according to manufacturer's directions. When the chocolate is semi-firm, remove from the machine into a covered container and stir in marshmallows and half of the broken crackers. When the vanilla is semi-firm, remove from machine and stir in the chocolate chips and the other half of the crackers. Chill both in the freezer until nearly solid.
Scoop some of each flavor into a third container, pressing together as you go, to create a marbled ice cream. Freeze until solid.
Recipe by Cooking With MicheleĀ® at https://cookingwithmichele.com/2012/07/smores-ice-cream-happy-fourth-of-july/