01 - Combine heavy cream and whole milk in a medium saucepan; heat over medium until steaming but not boiling.
02 - In a bowl, whisk granulated sugar and egg yolks until pale and slightly thickened.
03 - Slowly pour about 1 cup of the hot cream mixture into the yolks while whisking constantly to temper.
04 - Return the tempered yolk mixture to the saucepan with the remaining cream.
05 - Over low heat, stir constantly with a wooden spoon until the mixture thickens enough to coat the back of the spoon at approximately 170°F (77°C); avoid boiling.
06 - Remove from heat and stir in peppermint and vanilla extracts; add green food coloring if desired.
07 - Pass the custard through a fine-mesh sieve into a clean bowl; cool to room temperature, cover, and refrigerate for at least 3 hours until thoroughly chilled.
08 - Process the chilled custard in an ice cream maker following the manufacturer's instructions.
09 - Add mini chocolate chips near the end of churning and mix until evenly dispersed.
10 - Transfer ice cream to a lidded container and freeze for 2 to 3 hours until firm before serving.