01 - Combine heavy cream, milk, and half the sugar in a medium saucepan. Heat over medium heat until steaming, not boiling.
02 - Whisk egg yolks, remaining sugar, and salt in a separate bowl until pale and thick.
03 - Slowly pour 1/2 cup hot cream mixture into egg yolks while whisking constantly to temper.
04 - Gradually whisk tempered egg mixture back into the saucepan.
05 - Cook over medium-low heat, stirring constantly with a wooden spoon until custard thickens enough to coat the back of the spoon (170-175°F).
06 - Remove from heat and stir in peppermint extract, vanilla extract, and green food coloring if using.
07 - Pour custard through a fine mesh sieve into a clean bowl. Cool to room temperature, cover, and refrigerate at least 4 hours until thoroughly chilled.
08 - Churn chilled custard in an ice cream maker according to manufacturer instructions.
09 - Add chopped chocolate chips during the last few minutes of churning.
10 - Transfer ice cream to a lidded container and freeze at least 2 hours until firm.
11 - Scoop and serve immediately.