01 - Combine heavy cream and whole milk in a medium saucepan and heat over medium until steaming but not boiling.
02 - In a separate bowl, whisk together egg yolks and granulated sugar until pale and slightly thickened.
03 - Gradually add about 1 cup of the hot dairy mixture to the yolk mixture, whisking constantly to temper the eggs.
04 - Pour the tempered egg mixture back into the saucepan with the remaining dairy mixture.
05 - Cook over low heat, stirring constantly with a wooden spoon, until the custard thickens enough to coat the back of a spoon, reaching approximately 170°F.
06 - Remove from heat and stir in peppermint extract, vanilla extract, and a pinch of salt.
07 - Strain custard through a fine sieve into a clean bowl. Cool to room temperature, cover, and refrigerate for at least 2 hours until thoroughly chilled.
08 - Churn the chilled custard in an ice cream maker according to manufacturer instructions.
09 - When the ice cream is nearly finished, add crushed peppermint candies and continue churning to evenly distribute.
10 - Transfer ice cream to a freezer-safe container and freeze for at least 2 hours until firm.
11 - Serve scoops garnished with additional crushed peppermint candies if desired.