In a large mixing bowl, beat the heavy whipping cream until stiff peaks form.
In a separate bowl, whisk together the sweetened condensed milk, vanilla bean paste, vanilla extract, and salt until smooth.
Gently fold the whipped cream into the condensed milk mixture in three additions, being careful not to deflate the mixture.
Fold in the patriotic sprinkles, mini chocolate chips, and chopped brownie pieces until evenly distributed.
Transfer half of the mixture to a loaf pan or freezer-safe container.
Drizzle hot fudge over the ice cream layer, then add the remaining ice cream mixture. Drizzle with more hot fudge and use a butter knife to create swirls throughout.
Sprinkle the top with additional brownie pieces and patriotic sprinkles.
Cover tightly and freeze for at least 6 hours, or overnight for the best texture.
Let the ice cream sit at room temperature for 5 minutes before scooping.