In a small saucepan or microwave-safe container, heat caramel sauce until warm but not boiling, about 1 minute over medium heat or 20 seconds in the microwave on full power (100%). Add salt and stir to combine. Set aside.
In a medium bowl, whisk together peanut butter, sugar, cream, milk, and vanilla until peanut butter is mostly dissolved. Let sit 5 minutes, or until sugar is dissolved, then whisk again.
Pour into an ice cream maker and churn according to manufacturer's directions. Add salted caramel for the last 10 seconds of churning.
Transfer to an airtight, freezer-safe container and freeze at least 8 hours and up to 24, depending on how firm you would like the ice cream to be.
Note: Nutritional analysis is per 1/4-cup serving.