01 - Heat heavy cream and milk in medium saucepan over medium heat until just steaming, do not boil.
02 - Whisk egg yolks, sugar, and salt in separate bowl until pale and slightly thickened.
03 - Slowly pour 1 cup hot cream mixture into yolks while whisking constantly to temper.
04 - Return tempered yolk mixture to saucepan with remaining cream.
05 - Cook over low heat, stirring constantly with wooden spoon until mixture thickens and coats back of spoon (170–175°F), about 5–7 minutes.
06 - Remove from heat and stir in peppermint extract, vanilla extract, and food coloring if using.
07 - Pour custard through fine mesh sieve into clean bowl. Cool to room temperature, cover and refrigerate at least 4 hours until thoroughly chilled.
08 - Churn chilled custard in ice cream maker according to manufacturer's instructions.
09 - During last 2 minutes of churning, add chopped chocolate to disperse evenly.
10 - Transfer to lidded container and freeze at least 2 hours until firm before serving.