2 1/2 cups heavy cream
1 1/2 cups whole milk
6 large egg yolks
3/4 cup sugar
1/4 teaspoon salt
1 to 2 teaspoons peppermint extract
1/2 cup crushed candy canes or hard peppermint candy
Warm the cream, milk, sugar, and salt in a medium saucepan. Make sure the sugar and salt completely dissolve. Bring to a gentle boil over medium heat. Remove from the heat.
In a medium bowl, whisk together the egg yolks. Slowly pour some of the the warm milk mixture into the egg yolks, whisking constantly, then scrape the warmed egg yolks back into the saucepan.
Stir the mixture constantly over medium heat with a wooden or heatproof rubber spatula, scraping the bottom as you stir, until the mixture thickens and coats the spatula, about 5-7 minutes.
Remove from heat and stir until cool. Chill mixture in the refrigerator for 3 to 24 hours.
Add 1 t. peppermint extract, mix well, then taste. Add more as needed until you reach the desired level of peppermintiness. (Different peppermint extracts vary in strength. I used 2 teaspoons of McCormick peppermint extract, which was just the right amount for our taste.)
Freeze in your ice cream maker according to the manufacturer’s instructions. (For the Cuisinart, put the blade in so that the circle is at the top. Turn the machine on first and then pour in the ice cream.)
Fold in the crushed peppermint candy. Put in an airtight plastic container and place in the freezer for at least an hour, preferably several hours.