Chop the watermelon into cubes, then place in a blender and blend (the blended amount should fill a 1-½ quart blender). Pour into a bowl and set aside.
Cut the cucumber in half, and remove the seeds by scooping them out with a spoon. Peel the cucumber halves, then chop them into a few smaller pieces.
Chop the tomato into quarters. Cut off the ends of the shallots and peel them (or just peel the onion), then cut into quarters.
Blend the cucumber, tomato, shallots, and basil leaves until smooth. Pour the mixture into the container with the watermelon mixture and mix with a spoon until fully combined.
Stir in the red wine vinegar, salt, and a few dashes of hot sauce. Place in the refrigerator and chill for 2 to 3 hours, until cold. Serve garnished with a few drops of olive oil.
Total time: 2 hours 10 minutes. Serves