Refrigerate the shaved chocolate and cherries in separate bowls to keep them firm.
Warm the cream and milk together in a saucepan over medium-low heat.
Whisk the eggs until light and fluffy, then mix in the sugar until smooth.
Slowly pour about one-third of the warm cream mixture into the egg mixture while whisking to temper it.
Add the remaining cream mixture, return everything to the saucepan, and heat gently until it reaches 175°F.
Chill the custard completely until it cools to about 40°F.
Pour the mixture into your ice cream maker and churn according to the machine’s instructions.
Add the chilled chocolate and cherries during the last minute of churning, then freeze until the texture is just right.
