01 - Combine heavy cream and whole milk in a medium saucepan. Heat over medium until just steaming, avoiding boiling.
02 - In a separate bowl, whisk the egg yolks and granulated sugar until pale and thickened.
03 - Slowly add about 1/2 cup of the hot cream mixture to the egg yolks, whisking constantly to temper.
04 - Return the egg mixture to the saucepan. Cook over low heat, stirring constantly, until custard thickens enough to coat the back of a spoon (77–80°C).
05 - Remove from heat and stir in peppermint and vanilla extracts. Add red food coloring if desired.
06 - Strain custard through a fine mesh sieve into a clean bowl. Cool to room temperature, then cover and refrigerate for at least 4 hours or overnight.
07 - Churn the chilled custard in an ice cream maker following manufacturer instructions.
08 - During the final 2 minutes of churning, mix in the crushed peppermint candies.
09 - Transfer to a freezer-safe container with lid and freeze for at least 2 hours before serving.