Place the shaved chocolate and cherries in separate bowls. Refrigerate.
In a medium bowl, whisk eggs until light and fluffy, 1 to 2 minutes. Gradually whisk in the sugar until blended, and then for an additional minute. Add cream and milk and whisk to blend.
Place bowl in refrigerator until ready to make ice cream. Add the mixture to an ice cream maker and follow the manufacturer’s directions to churn ice cream. Approximate churning time: 25 minutes. Two minutes before ice cream is finished church, add the chocolate shavings and cherries.
Transfer ice cream to an airtight container and place in the freezer for a minimum of 2 hours.