Put the watermelon in the jar of a blender. Whisk together salt and the watermelon. Add the lime juice and olive oil. Cover and puree briefly, retaining a little bit of texture.
Add the green pepper, the cucumber, the tomatoes, the onion and cilantro and run the blender just for a few seconds to mix. Refrigerate until chilled, at least 1 hour. Stir, taste and adjust seasoning. Add sufficient cold water to get the perfect mixture and texture.
To serve, divide among serving bowls or glasses and garnish with a drizzle of olive oil, avocado, chopped green pepper and cilantro and serve immediately.