If you want to make this without an ice cream maker, simply let the mixture chill; instead of processing it in an ice cream maker, whisk or stir the mixture and place it in a freezer-safe container. Every 30-45 minutes, stir or whisk the mixture again until it becomes thick, leaving it to sit lightly covered in between. Once the mixture is thick, you can add the crushed peppermint candy and let it chill for 4-6 hours, and then enjoy!