In a large saucepan, combine everything except the peanut butter and the peanut butter cups. Whisk to combine and then heat over medium heat, stirring continually, until it comes to a full boil. If you are impatient like me, increase the heat, but continue stirring non-stop. Do not step away at this point.
When the mixture begins to foam, remove it from the heat and stir in the peanut butter. Whisk it together until it is fully incorporated. Cover and refrigerate at least 8 hours or up to two days.
Process according to your machine's instructions. When the ice cream is almost finished, stir in the candy pieces and transfer to a freezer-safe container.
