Start by heating the 4 cups of whole milk and tablet of Mexican chocolate over medium heat in a pan on the stove. Heat and stir until the chocolate is all melted and incorporated into the milk. (It will look spotty on top. That is o.k.)
Pour 1 1/2 cups of the hot chocolate into a mixing bowl and add the sugar. Stir until the sugar is dissolved. Put into the refrigerator for about an hour to chill. Then add the remaining ingredients, and stir well (I use a wire whisk). Then you can either chill the mixture longer (even overnight) or pour it directly into your ice cream maker and follow the manufacturer's directions.
Transfer to an airtight container and put into the freezer.