Stir 1 cup caramel sauce, condensed milk, and salt together until well-combined.
Using an electric mixer on high speed, beat heavy cream in a separate bowl until stiff peaks form.
Using a rubber spatula, fold caramel mixture into whipped cream (you may need to use the electric mixer on low-speed at first to help get things started).
Fold in brownie pieces.
Transfer to a 9" bread pan and swirl with remaining 1/4 cup caramel sauce
Cover with clear wrap and freeze at least 6 hours (preferably overnight) before serving.
No-churn ice cream melts a bit faster than regular ice cream, keep this in mind when serving.