Beat cold heavy dairy cream on medium in a stand mixer fitted with the whisk attachment (or using a hand mixer) until stiff peaks form.
Turn down the speed a little and pour the condensed milk into the whipped cream. (Stir in vanilla extract now if desired).
Then, turn up the machine speed again and whip until your mixture is thick and to stiff peaks.
Now you have your ice cream base add the melted cooled chocolate. Do this as quickly as you can, stirring constantly to keep the chocolate from seizing up and separating from the ice cream base. Once the chocolate has been mixed through, fold in the crushed peppermint candy.
Freeze at least 4 hours or overnight before scooping and serving.