Put the yolks with the sugar in a saucepan and mix them. Gradually add the milk, stirring constantly until all the milk is incorporated. Put the mixture on the fire, let the heat be low, stir continuously with a whisk, until the sweetener melts.
Remove the pan from the heat, add the chocolate, carob and turn until all is well incorporated. Cover with foil, cool the chocolate cream.
Cream for whipped cream, cold, mix it until it starts to become frothy. Add the mixture of chocolate, vanilla, rum and mix until all are incorporated. You will get a frothy and very aerated cream.
Prepare a casserole, pour the ice cream composition, cover it with the lid. Put it in the freezer, and after 30 minutes take it out, mix it with a silicone paddle and put it back in the freezer.
Do this 3 times, after 30 minutes. After mixing it 3 times, do not walk on it until the next day.
When serving, remove it about 15 minutes before at room temperature, so you can take it nicely with a special cup for ice cream.
Enjoy your meal!