In a large bowl or the bowl of your ice cream maker, add heavy whipping cream, half-and-half, 2 cups sugar, 1/4 teaspoon salt, 1 tablespoon vanilla, and 1/4 teaspoon peppermint extract. Stir it together well until sugar is well incorporated. 

In a food processor or blender, finely crush about 12-14 full size candy canes. You want about 8 ounces of candy ground up pretty well. How many candy canes you use depends on what size they are.

Add 8 ounces of finely crushed candy to the bowl with the cream. Stir well.

While you have the food processor out, use it to coarsely crush another 3-5 candy canes. You want to get between 1/3 and 1/2 cup, how much you use is your preference. Crush them into small to medium chunks, the size that you might like to bite into when you're eating your ice cream later. Set aside. You won't need these coarsely crushed ones until after your ice cream is churned, I just didn't want you to clean out your food processor and then curse my name later when I told you to get it out again. 

Add the cream mixture to the bowl of your ice cream maker if you didn't mix it there in the first place. Churn ice cream according to your ice cream maker's instructions. Mine takes about 40 minutes. The ice cream should be thick and about the consistency of soft serve. 

Use a long spoon to stir in 1/3 or 1/2 cup coarsely crushed candy canes. 

Transfer the mixture to a large tupperware or baking dish with a lid. A 9x5 inch bread pan would work. 

Cover well and freeze for several hours, at least 3-5, but 8 hours is best, or overnight. 

Serve as is or with additional crushed candy canes! This ice cream is AMAZING when paired with Nana's Famous Fudge Brownies!