In a medium saucepan, heat the half-and-half over medium-low heat until it just begins to simmer.

While the half-and-half is heating, whisk together the egg yolks and sugar in a medium bowl.

Remove the hot half-and-half from the stove and gradually pour it into the egg yolk mixture, whisking constantly as you pour.

Return the mixture to the saucepan and heat over medium-low heat, stirring constantly, until the mixture thickens and coats the back of a wooden spoon (~4-5 minutes).

Remove the mixture from the stove and pour through a fine mesh strainer into a clean container. (Tip: Use a spoon or spatula to help push the mixture through the strainer.)

Add the vanilla extract, peppermint extract and heavy cream to the strained mixture; stir until well combined. Cover mixture with plastic wrap, pressing the plastic directly onto the surface of the mixture. Refrigerate overnight.

Pour the ice cream mixture into an ice cream maker and freeze according to the manufacturer’s directions. About 5 minutes before the ice cream is done (while it’s solid, but still soft), add the crushed candy canes.

Place the finished ice cream into the freezer to harden for at least 4-6 hours before serving.

Garnish with additional crushed candy canes before serving (optional).