The Preparation
Heat milk and 1 cup of the cream with sugar in a saucepan over medium heat until steaming.
Whisk egg yolks in a bowl, then slowly temper in the hot milk mixture.
Return to saucepan and cook over low heat, stirring constantly, until custard coats the back of a spoon (170-175°F).
Remove from heat, strain, and stir in peppermint extract and remaining cup of cream.
Chill custard completely in the refrigerator (at least 4 hours or overnight).
Churn in an ice cream maker according to manufacturer instructions.
Fold in crushed peppermint candies during the last few minutes of churning.
Freeze in a container for at least 2 hours before serving.