Add the peanut butter, sugar, milk, heavy cream, vanilla extract, and salt to a large bowl, and stir them together for a few minutes, to help the sugar dissolve a bit.
Pour the mixture into the 2 Qt ice cream maker and allow to run for 25 to 30 minutes, according to the directions of your machine.
Add the chopped up peanut butter cups into the ice cream maker, and let it continue to run for another 3 to 5 minutes, until they are mixed throughout.
Add the peanut butter to a small microwave safe bowl, and microwave for 30 seconds.
Scoop about 1/4 of the ice cream into a 2Qt pan, and drizzle about 1/4 of the peanut butter over the top. Swirl it in with a knife. Repeat with more ice cream, more peanut butter, more ice cream, more peanut butter, more ice cream.
Cover the pan with plastic wrap or foil, and place the pan in the freezer for at least 6 hours, up to overnight.