Needless to say, be sure to use peppermint candy canes, not the gross fruit-flavored ones.
2 large eggs
3/4 cup (150 g) granulated sugar
2 cups (500 ml) cups heavy cream
1 cup (250 ml) milk
1½ teaspoons peppermint extract
½ teaspoon vanilla extract
4 to 5 peppermint candy canes
In a large bowl, whisk the eggs for 1 to 2 minutes. Whisk in the sugar a little at a time, then whisk for 1 minute more. Pour the cream, milk, peppermint extract, and vanilla into the egg mixture and whisk for another minute until the sugar is dissolved. Freeze in an ice cream maker according to the manufacturer’s instructions (usually spin for 25 minutes).
While the ice cream is churning, put 4 to 5 peppermint candy canes into a resealable plastic bag and zip it tight. Smash them with a can into pieces 1/4-inch (6-mm) or smaller. During the last five minutes of churning, add the candy pieces. Spoon into a freezer-safe container and freeze until scoopable, at least 6 hours.
Author's Note: I make my ice cream the old-fashioned way: with fresh, local, raw eggs. You are under no obligation to do the same. If you're worried about salmonella, your options are many: Use pasteurized eggs instead. Or leave out the eggs entirely for a perfectly good Philadelphia-style ice cream. Or pull out your favorite cooked custard-style ice cream cookbook (like David Lebovitz's The Perfect Scoop) and modify this recipe using egg yolks and a thermometer. Or pull out your favorite cornstarch-based, egg-free ice cream cookbook (like Jeni's Splendid Ice Cream at Home) and modify her base. It's your kitchen after all.