Puree the watermelon in a food processor or blender. Place a fine mesh sieve over a mixing bowl. Transfer the pureed watermelon to the sieve to strain off the juice. Discard the pulp. Separate 3/4 cup of the watermelon juice for making the simple syrup.Prepare the Watermelon-Basil Simple Syrup
In a small saucepan stir together the 3/4 cup of watermelon juice and the sugar. Bring this to a boil over medium-high heat.
Add 1 cup of packed basil leaves to the simple syrup and allow the leaves to steep for 15 minutes. Make the Sorbet Base
Once the basil has steeped, strain the simple syrup into the bowl containing the rest of the watermelon juice, and whisk to incorporate.
Add the lime juice, Chambord (if using), vodka, and salt to your sorbet base. Whisk this together. Allow this base to chill in the fridge for 4-24 hours.
Prior to churning, stir in the minced basil. Freeze the Sorbet
In your ice cream machine, churn the sorbet for 15-20 minutes, or according to the manufacturer's recommendation for sorbet. It should look somewhat like a slurpee when it's done churning. It will harden more as it freezes.
Once the sorbet is the proper consistency, transfer it into an ice cream container and allow it to firm up for 2-3 hours before serving and enjoying.