In a mixing bowl, whisk together the heavy cream, whole milk, granulated sugar, and vanilla extract until the sugar is dissolved.

Add the creamy peanut butter and chocolate syrup, and whisk until fully combined and smooth.

Cover the mixture and refrigerate for at least 2 hours or until thoroughly chilled.

Pour the chilled mixture into an ice cream maker and churn according to the manufacturer's instructions until it reaches a soft-serve consistency.

During the last few minutes of churning, add the chopped peanut butter cups.

Transfer the ice cream to a freezer-safe container and freeze for at least 2 hours to firm up.