Blanch the basil leaves in boiling salted water for 5 seconds, then place in an ice bath. Drain and wring the basil dry in a dish towel. Chop coarsely.
In a food processor, puree the basil with salt, vitamin C and just enough softened ice cream to make a puree (about 3 tablespoons). You should have about 1 cup basil puree. Add the remaining ice cream and puree. Quickly take the finished pureed ice cream and transfer it from the processor back to the freezer container. Add chocolate and mix in thoroughly. Place container in freezer. Freeze for at least 1 hour.