01 - Combine heavy cream and whole milk in a medium saucepan and heat over medium heat until just steaming, avoiding boiling.
02 - In a separate bowl, whisk egg yolks and granulated sugar until pale and slightly thickened.
03 - Gradually whisk about 1/2 cup (120 ml) of the hot cream mixture into the egg yolks to temper them, then slowly whisk the tempered egg mixture back into the saucepan with the remaining cream.
04 - Cook over medium-low heat, stirring constantly with a wooden spoon, until the custard thickens enough to coat the back of the spoon (77–80°C / 170–175°F). Do not boil.
05 - Remove from heat and stir in peppermint extract, vanilla extract, and a pinch of salt.
06 - Pour the custard through a fine-mesh sieve into a clean bowl. Allow to cool to room temperature, then cover and refrigerate until thoroughly chilled, at least 2 hours.
07 - Churn the chilled custard in an ice cream maker following the manufacturer's instructions.
08 - When the ice cream is nearly finished churning, fold in the crushed peppermint candies.
09 - Transfer the ice cream to a lidded freezer-safe container and freeze until firm, about 4 hours.
10 - Allow the ice cream to sit at room temperature for 5–10 minutes before scooping and serving.