In a small saucepan, heat heavy cream and basil until just simmering. Take off the heat and let basil steep for 30 minutes. Place the mixture in a blender and blend until basil is chopped, but make sure not to over whip the cream (I used an immersion blender which worked nicely).

Fill a large bowl with ice and fill 1/3 full with water to create an ice bath. Place a smaller bowl inside the ice bath. Pour basil-cream mixture into the smaller bowl, let sit until cool, and then refrigerate until chilled, about 1 hour. (You can also skip the ice bath and put the slightly cooled basil mixture in the fridge overnight, and then proceed to blending.)

In a medium bowl, stir together condensed milk, vanilla, and salt. In a large bowl of a standing mixer, beat the basil-cream on high until stiff peaks form, about 3 minutes. With a rubber spatula, gently fold 1/3 of the whipped cream into condensed milk mixture. Fold until fully combined. Gently fold in the rest of the whipped cream. Pour into a regular sized loaf pan, and freeze until firm, 6 hours [or, covered, up to 1 week].