In a medium saucepan, combine the sugar, water, ginger and thyme. Set over moderate heat and bring to a simmer. Cook until the sugar has dissolved. Remove from the heat and transfer to a pitcher or measuring cup. Set aside to cool.

Place the watermelon in a blender and purée until smooth. Pour into a large measuring cup or pitcher, through a fine mesh strainer, to remove the pulp. Chill in the fridge until ready to use. This will make enough juice for about 8 cocktails.

Coat the rim of a coupe glass with a bit of lime juice and then dip in a bit of salt. In a cocktail shaker, combine the white rum, lime juice, 1 tablespoon of the simple syrup, and 3 tablespoons of watermelon juice. Fill with ice, cover and shake vigorously until well-combine and thoroughly chilled, about 15 seconds. Strain into the prepared coupe glass and garnish with a watermelon wedge. Enjoy!