Place a 9x5-inch loaf pan in the freezer to chill.
To the bowl of a stand mixer, add the heavy cream. Start mixing at the lowest speed, and then gradually increase speed to medium until the cream starts to get thicker. (The gradual progression prevents you from spraying yourself with cream.)
The cream will thicken and start to peak. Mix on high speed until the cream is thick and stiff. This happens quickly, so watch it closely!
In a medium bowl, combine sweetened condensed milk, peppermint extract, salt, food coloring, and 1 cup of whipped cream.
Add the chocolate pieces and the sweetened condensed milk mixture back into the mixing bowl with the rest of the whipped cream. Gently fold the ingredients together.
Pour the mixture into the chilled pan and freeze for at least 5 hours, or until fully set up, before serving.