01 - Heat the heavy cream and milk in a medium saucepan over medium heat until steaming, avoiding boiling.
02 - Whisk egg yolks, sugar, and salt in a separate bowl until pale and slightly thickened.
03 - Gradually whisk 1 cup of hot cream into the yolks to temper, then return mixture to the saucepan.
04 - Cook over low heat, stirring constantly with a wooden spoon until thickened and coating the spoon back (170–175°F), approximately 5–7 minutes.
05 - Remove from heat and stir in peppermint extract, vanilla extract, and food coloring if desired.
06 - Pour through a fine mesh sieve into a clean bowl. Cool to room temperature, cover, and refrigerate at least 4 hours until thoroughly chilled.
07 - Churn the chilled custard in an ice cream maker following manufacturer instructions.
08 - During the final 2 minutes of churning, add chopped chocolate for even distribution.
09 - Transfer to a lidded freezer-safe container and freeze at least 2 hours until firm before serving.