01 - Combine heavy cream and whole milk in a medium saucepan. Heat over medium until steaming but not boiling.
02 - Whisk egg yolks and granulated sugar in a bowl until pale and slightly thickened.
03 - Gradually whisk 1/2 cup of the hot cream mixture into the egg yolk mixture to temper. Then whisk tempered yolks back into saucepan with remaining cream.
04 - Cook over medium-low heat, stirring constantly with a wooden spoon, until mixture thickens enough to coat the back of the spoon at 170–175°F (77–80°C). Avoid boiling.
05 - Remove saucepan from heat. Stir in peppermint extract, vanilla extract, and salt.
06 - Pass custard through a fine-mesh sieve into a clean bowl. Cool to room temperature, cover, and refrigerate at least 2 hours.
07 - Churn chilled custard in an ice cream maker according to manufacturer’s instructions.
08 - In the final moments of churning, incorporate the crushed peppermint candies.
09 - Transfer to a lidded container and freeze until firm, approximately 4 hours.
10 - Allow ice cream to soften at room temperature for 5 to 10 minutes before scooping and serving.