Preheat a grill to high heat (400 degrees F). To grill the watermelon, first sprinkle with the sugar and salt. Grill quickly, cooking each side for 2 minutes and flipping with a wide spatula. Once the watermelon is cooked, remove from the grill and add to a blender, along with the yogurt, apple juice, ice, honey and vanilla. Puree until smooth, 1 to 2 minutes. Finally, add the mint and basil leaves, pulse 5 to 6 times and serve. Garnish with watermelon wedges and mint.