In a blender, puree 4 cups chopped watermelon with the chopped tomato, three-quarters of the cucumber, 2 tbsp. EVOO and the red wine vinegar; season with salt and pepper.
Chop one of the tomato halves and the remaining cucumber. Toss in a small bowl with the remaining 1 cup chopped watermelon; season.
In another small bowl, whisk 2 tbsp. EVOO with the basil. Rub the toasts with the cut side of the remaining tomato half and top with the prosciutto. Discard the tomato skin.
Divide the soup among bowls. Garnish with the chopped watermelon mixture, basil oil and coarsely ground pepper. Serve with the prosciutto toasts.