To a blender, add 3 cups of the watermelon. Roughly chop 2 tomatoes, three-quarters of the cucumber, half of the bell pepper, and a quarter of the onion and add them to the blender. Add the garlic, vinegar, salt, pepper, and hot sauce (if using). Blend on high speed until the soup is very smooth.
With the blender running, slowly pour in the oil and blend until the mixture is thoroughly combined and emulsified.
Transfer the soup to an airtight container and refrigerate for at least 2 hours and up to 12 hours.
Meanwhile, finely chop the remaining tomato, half bell pepper, quarter cucumber, quarter onion, and ½ cup watermelon. Combine in a small bowl, cover, and refrigerate until ready to serve.
Before serving, whisk the soup and taste and adjust for vinegar, salt, and hot sauce. Ladle into serving bowls and top with a big scoop of the chopped watermelon mixture. Sprinkle with mint and drizzle with oil, if you like. Serve with grilled bread.