Step 1

Whisk half-and-half, cream, sugar, peppermint extract, and kosher salt in a small bowl to combine; chill ice cream base in freezer 15 minutes.

Step 2

Fill a 1-gal. resealable plastic bag two thirds of the way with ice (4–8 cups, depending on the size of your ice). Add rock salt, close bag, and shake to combine. Remove ice cream base from freezer and stir to incorporate any sugar at the bottom of the bowl. Pour into a sandwich-size resealable plastic bag and close. Place into larger bag with ice. Seal larger bag and shake and smush ice around until ice cream is firm, 10–12 minutes.

Step 3

Remove ice cream from bag of ice. (If it is too firm to scoop from bag, massage with your hands for a minute to soften ice cream.) Scoop ice cream into a clean small bowl. Using a toothpick, add food coloring to ice cream, dragging it through to create streaks. Top with candy cane pieces.