In a medium bowl, combine sweetened condensed milk, cocoa powder, vanilla and salt; stir and set aside.
In the bowl of a stand mixer, add heavy cream and process until stiff peaks form.
Fold a third of the whipped cream into the milk-chocolate mixture then add it to the remaining heavy cream, folding gently. Add dark and white chocolate pieces including any dust or slivers left on the cutting board; gently fold inches.
Pour the mixture into a 2 quart ice cream tub, cover and transfer to the freezer for at least 12 to 24 hours or until frozen.
