In a medium mixing bowl with electric mixer on low speed, combine the peanut butter and sugar until smooth. Add the milk and mix on low speed until the sugar is dissolved, about 1-2 minutes. Stir in the heavy cream and vanilla. Cover the mixture and refrigerate 1-2 hours to chill it down. May be left in refrigerator over night.
Follow your ice cream maker's directions to freeze this ice cream. I have a Cuisinart, which says to turn on the ice cream maker; pour the mixture into the freezer bowl and mix until thickened, about 15-20 minutes. Five minutes BEFORE mixing is complete, add the chopped candy bars through the top and let mix in completely.
Ice cream will have a soft, creamy texture and can be eaten right away if soft serve is what you like. Or, place the ice cream in an airtight container in the freezer for about 2 hours. If too hard, remove from freezer about 15 minutes before serving.