Blend blackberries, sweetened condensed milk, vanilla, and salt until smooth; optionally strain seeds.

Whip cold heavy cream to stiff peaks, about 3 to 4 minutes.

Fold whipped cream into blackberry mixture in thirds, leaving streaks, then transfer to a loaf pan and swirl extra purée on top.

Cover and freeze until firm, at least 6 hours. Let soften at room temperature for 5 minutes, then scoop and serve.