In a medium mixing bowl, use a hand mixer or whisk to combine the peanut butter and sugar until smooth. Add the milk and mix on low speed until the sugar is dissolved, about 1 to 2 minutes. Stir in the heavy cream and vanilla.
Turn the machine on; pour the mixture into freezer bowl, and let mix until thickened, about 25 to 35 minutes. Five minutes before mixing is completed, add the chopped candy through the top and let mix in completely. The ice cream will have a soft, creamy texture.
If a firmer consistency is desired, transfer the ice cream to an airtight container and place in freezer for about 2 hours. Remove from freezer about 15 minutes before serving.