Chill the ice cream bowl for at least 24 hours or until solid. You should not hear any water sloshing around when you shake the bowl.
In a large saucepan over medium heat, whisk together the heavy cream, whole milk, unsweetened cocoa powder, granulated sugar, and salt.
Bring the cream mixture to a simmer. Watch for small bubbles to appear along the edges of the pot. Do not bring to a boil.
Once simmering, add in half of the creamy peanut butter (1/2 cup) and half of the chopped semi-sweet chocolate (2oz). Stir until the peanut butter and chocolate are melted.
Pour the mixture into a large glass bowl. Stir in the vanilla extract.
Cover the surface of the ice cream base with plastic wrap and chill the mixture for at least 4 hours.
Add the ice cream base to the bowl of an ice cream maker. Churn according to the manufacturer’s instructions.
In the last 2 minutes of the churn, add the chopped peanut butter cups and remaining chopped chocolate (2 oz). Reserve 1/4 cup of the chopped peanut butter cups for topping.
Spoon half of the ice cream into a loaf pan. Add half of the remaining peanut butter in dollops. Swirl with a knife. Repeat with remaining ice cream and peanut butter. Top with reserved chopped peanut butter cups, pushing them into the surface.
Freeze for at least 4 hours or until firm.
Let the ice cream sit at room temperature for 5 minutes before scooping. Serve immediately.