In a medium saucepan over medium heat, combine the heavy cream, whole milk, half of the sugar, and salt. Stir occasionally until the mixture begins to steam, but make sure it doesn't boil.
In a separate bowl, whisk the egg yolks with the remaining sugar until the mixture is pale and slightly thickened.
Slowly pour the warm cream mixture into the egg mixture while whisking continuously. This step is crucial to avoid cooking the eggs too quickly and creating lumps.
Pour the combined mixture back into the saucepan and place it over medium heat. Stir constantly with a wooden spoon until the mixture thickens enough to coat the back of the spoon. This forms a custard base. Be patient; this step usually takes a few minutes.
Remove the saucepan from heat and strain the custard through a fine-mesh sieve into a large bowl. This step ensures a smooth ice cream base.
Stir in the vanilla extract and peppermint extract. For that extra holiday flair, add a few drops of red or pink food coloring if desired. The result will be a beautiful pink peppermint ice cream!
Cover and put in the fridge for at least two hours, but I would do overnight
Take out of the fridge and make it according to the manufacturer’s instructions. (I always use my Cuisinart Ice Cream Maker)*
While the ice cream is churning, take your candy canes or peppermint candies and crush them into small pieces. This can be done by placing them in a plastic bag and using a rolling pin or a meat mallet to break them into small bits.
Once the ice cream has reached a soft-serve consistency, gently fold in the crushed peppermint candies. The small pieces will add bursts of peppermint flavor and a delightful crunch to every bite.
Wow everyone by serving it immediately or store in an airtight container in the freezer for up to 2 weeks.