In the bowl of a stand mixer, add cocoa powder, granulated sugar, brown sugar, and milk. Whisk until sugars dissolve. Add heavy cream and vanilla and whisk until thick and fluffy, about 3 minutes. You'll know it's done when the mixture is the consistency of pudding.
Cover with plastic wrap and place in the refrigerator for an hour.
Remove from the refrigerator and transfer the mixture to the bowl of your ice cream maker. Churn for 15 minutes.
Add half of the mixture to a bowl. Top with half of the peanut butter sauce and peanut butter cups. Swirl with a knife. Top with remaining ice cream. Swirl in the remaining peanut butter sauce and peanut butter cups. Cover and place in the freezer until completely frozen, about 4 hours.
Peanut Butter Sauce: In a small bowl, add peanut butter and powdered sugar. Whisk to combine. Whisk in half & half, milk, and vanilla until smooth.
Recipe by The Messy Baker Blog at http://themessybakerblog.com/2013/01/13/chocolate-peanut-butter-cup-ice-cream-sundaysupper/