Warm the milk, sugar, and salt in a medium saucepan over medium heat to dissolve the sugar and salt completely.

Pour the cream into a metal bowl set in a larger bowl of ice, and set a medium-mesh sieve over the top.

In a separate bowl, whisk together the egg yolks. Very slowly pour the warmed milk mixture into the egg yolks, whisking constantly, to temper the egg yolks. Then scrape the warmed milk and egg yolks mixture back into the saucepan.

Stir the mixture constantly over medium heat with a wooden spoon, scraping the bottom as you stir, until the mixture thickens and coats the spoon, about 5-7 minutes. Do not let the mixture get too hot that it starts to cook/scramble the egg.

Pour the custard through the sieve, into the cream below. Stir the mixture over the ice bath until cooled. Then place mixture in the fridge to cool thoroughly.

Once the mixture is thoroughly chilled, stir in the peppermint extract. Because peppermint extracts can vary in strength, start out with 1 teaspoon and give it a taste test. If you'd like more peppermint flavor, add a 1/4 teaspoon at a time, until you reach the desired level of peppermint flavor. I use McCormick brand pure peppermint extract, and add between 2 and 2½ teaspoons when I make this ice cream.

Freeze mixture in an ice cream maker according to the manufacturer’s instructions.

When the ice cream is formed in the ice cream maker, and still fairly soft, fold in the crushed peppermint candy.  

Transfer the ice cream to an airtight plastic container and place in the freezer for at least an hour (will still be quite soft), preferably for several hours or overnight. If the ice cream is frozen overnight or longer, you may need to let it sit at room temperature for a few minutes to soften it before serving.