Special equipment: 9-by-5-by-3-inch metal loaf pan
Put a 9-by-5-by-3-inch metal loaf pan in the freezer to chill. Put the chocolate-peppermint candies and 3/4 cup of the heavy cream in a medium saucepan over medium heat and cook, stirring frequently, until the candies are melted, about 5 minutes. Cool completely.
Meanwhile, whip the remaining 2 cups heavy cream in a large bowl with an electric mixer on medium high until firm peaks form, about 2 minutes. Pour the condensed milk into a medium bowl and fold in 1 cup of the whipped cream with a rubber spatula until combined, then fold the lightened mixture back into the whipped cream until well blended. Gently fold in the marshmallows.
Remove 2 tablespoons of the chocolate sauce and set aside. Pour a third of the ice cream mixture into the chilled pan, then top with half of the remaining chocolate sauce. Repeat with one-third more of the ice cream mixture, then the remaining chocolate sauce. Cover with the remaining ice cream mixture and sprinkle the crushed peppermint puffs on top. Drizzle the top with the reserved chocolate sauce. Loosely cover with plastic wrap and freeze until solid and scoopable, about 3 hours and up to overnight. Serve in a cup with a candy cane if using.
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