Heat half-and-half in a sauce pan over medium heat to steaming or 170°F, about ten minutes. Remove from heat and set aside.

In a large bowl, whisk together egg yolks and sugar.

While whisking the egg yolk mixture vigorously, slowly add hot half-and-half. Once added, return the mixture to the saucepan.

Heat mixture over medium heat, whisking continuously, until thickened or 170°F. Remove from heat.

More mixture into a large bowl, whisk in cream, peppermint, and salt. Cover with plastic wrap and refrigerate at least 8 hours.

Set up ice cream maker and churn according to manufacturer's directions.

Fold in crushed candy canes, transfer to an airtight container and store in freezer.