Prepare the simple syrup. Simple syrup is made of equal parts sugar and water. Bring to a boil, reduce the heat, and then simmer until all the sugar is dissolved. It's great for drinks, and lasts for a long time in the fridge, so I always make extra. Allow to cool to room temperature before adding to the sorbet mixture.
In a food processor or blender, puree the watermelon.
Strain the watermelon through a sieve (to remove seeds and any remaining large chunks). You want 4 cups total strained watermelon puree for the sorbet.
Add about a cup of the watermelon puree back into the food processor.
Add the 1/2 cup basil, and puree until the basil chopped into little pieces.
Pour the watermelon-basil mixture back with the rest of the watermelon puree.
Stir in the lime juice and the vodka.
Stir in the cooled simple syrup.
Add the mixture to your ice cream/sorbet maker, and follow manufacturer instructions until frozen.
Serve immediately for a softer sorbet, or place in the freezer for a harder sorbet later on.
When it's time to serve, sprinkle individual servings with a good pinch of Fleur de sel and garnish with a sprig of basil.