Place melon, tomatoes, peppers and scallions in a blender, and puree until smooth. You made need to stop once or twice to scrape down the sides of the blender to ensure everything is uniformly blended.
Keep the blender on and add the vinegar and kosher salt, then slowly stream in the olive oil. Keep blending until it becomes pale and frothy. Taste and adjust seasoning if needed.
Pour into a bowl, large Mason jar or other vessel and chill for several hours.
Garnish with reserved melon, olive oil and flaky salt before serving.