In a large, heavy saucepan, combine the cream, milk, sugar, and salt. Bring to a boil over medium-high heat and cook, stirring often, until the sugar has dissolved.

In a bowl, whisk the yolks together until they change to a lemon color. Gradually whisk about 1 cup of the hot milk mixture into the yolks. Now, whisk the yolk mixture into the hot milk mixture and continue to cook, stirring constantly, until the mixture thickens enough to coat the back of a metal spoon.

Refrigerate for 2 to 3 hours. Add the peppermint extract, stirring well.

Freeze in an ice-cream maker according to the manufacturer’s instructions.

When the ice cream is partially frozen, stir in the candies.