Make the base: In a medium mixing bowl, use an electric mixer to combine peanut butter and sugar until smooth. Add milk and mix on low until sugar is dissolved- a full two minutes. You don’t want to be tasting crunches of sugar in your ice cream, so give it a chance to dissolve. Mix in heavy cream and vanilla and beat until well combined and smooth.
Process the ice cream: Turn on your ice cream machine, pour the base in the freezer bowl, and let mix until thickened, about 25 to 30 minutes. A couple of minutes before you’re ready stop the mixing, add in the chopped peanut butter cups. The ice cream will be a soft-serve consistency. You can eat it right away, or freeze to eat later. If you freeze it for later, it will be more ice-cream-scoopable. Let it sit out for a few minutes before you try to scoop it.