Pour the cold heavy cream into a large bowl or jar. Set aside.

Separate 4 egg yolks from the egg whites and place the egg yolks into a heat-safe bowl. (Refrigerate or freeze the egg whites for later use).

In a bowl, whisk together the egg yolks with sugar, sea salt and set aside.

Add the milk to a medium saucepan or pot and simmer over low heat until scalding hot.

While whisking the egg mixture, gradually pour in the warmed milk (known as tempering the eggs).

Pour the mixture back into the saucepan and cook over low-medium heat, until the custard thickens. When you can draw a line on the back of a spatula or wooden spoon, the ice cream mixture is ready.

Remove pan from the heat and stir in peppermint extract (and vanilla extract, if using).

Pour the ice cream mixture through a sieve into the cold heavy cream.

Give the mixture a stir and cover with a lid/plastic wrap.

Place into the refrigerator to chill for at least 6-8 hours, or overnight.

The next day, churn the ice cream according to your ice cream manufacturer's instructions.

In the last 5 minutes of churning, add in the crushed candy cane pieces.

Transfer the churned ice cream to an airtight container and place into the freezer.

Freeze the ice cream for at least 6-8 hours, or until firm.

Sprinkle additional crushed peppermint candy cane pieces before serving, if desired.