In a medium saucepan over medium heat, warm the milk and heavy cream to 140 degrees.
As the milk heats, in a seperate bowl, beat the eggs until smooth and creamy, about 3 to 5 minutes.
Very slowly add the sugar to the eggs and beat until the sugar is dissolved.
While beating the eggs and very slowly, temper the eggs by adding about ⅓ of the heated milk to the eggs. Then, whisk the egg mixture to the remaining milk in the pot.
Heat the liquid until 175 degrees, stirring often. Remove from heat and refrigerate overnight.
Pour the mixture into the ice cream maker and freeze according to the manufacturer's instructions.
When the ice cream is almost completely set, stir in the chocolate and cherries.
For firmer ice cream, transfer ice cream to a freezer-safe container and freeze for 4 to 6 hours.
Makes about 2 quarts frozen.
Note: Frozen or canned cherries can be substituted but should be drained first. One batch of ice cream was too much for the Cuisinart 2 quart machine, so I removed some of the ice cream as it froze and began overflowing.