01 - Combine heavy cream, whole milk, and half of the sugar in a medium saucepan. Heat over medium heat until the mixture just begins to steam, avoiding a boil.
02 - Whisk egg yolks with the remaining sugar in a mixing bowl until the mixture becomes pale and slightly thickened in texture.
03 - Gradually pour approximately 1 cup of the hot milk mixture into the egg yolks while whisking continuously to prevent curdling and temper the eggs.
04 - Return the tempered yolk mixture to the saucepan. Cook over low heat, stirring constantly with a wooden spoon until the custard thickens enough to coat the back of the spoon, reaching 170–175°F.
05 - Remove from heat immediately. Stir in peppermint extract, vanilla extract, and green food coloring until fully incorporated throughout the custard.
06 - Pour the custard through a fine mesh sieve into a clean bowl to eliminate any cooked egg bits. Allow to cool to room temperature, then cover and refrigerate for at least 4 hours until thoroughly chilled.
07 - Process the chilled custard in an ice cream maker according to manufacturer instructions. Add the chopped chocolate chips during the final 2-3 minutes of churning.
08 - Transfer the churned ice cream to a freezer-safe container. Freeze for a minimum of 2 hours until firm enough to scoop.
09 - Scoop into bowls or cones and serve immediately. Garnish with additional chocolate chips or fresh mint leaves if desired.