Whisk the half and half, cocoa powder, sugar, and salt in a large saucepan. Bring to a boil over medium-high heat. Immediately remove from heat and whisk in the peanut butter until smooth and completely incorporated.
Spoon the mixture into a large resealable container and allow to cool in the refrigerator completely (about 4 hours). Meanwhile, dream of all the things you can do with this amazing homemade ice cream.
When fully chilled, churn the ice cream in your ice cream maker according to the manufacturer's directions. Add the peanut butter cookies and mini peanut butter candies just a few minutes before the ice cream is fully set.
Spoon into a container. I topped with some bonus cookie and candy bits. Cover and allow to set in the freezer over night (8 hours). Grab a spoon and enjoy.