In a large salad bowl toss together lettuce, arugula, watercress, and basil; set aside. Pit, peel, and slice mangoes. Chop enough of the sliced mangoes to make 1/2 cup; set remaining sliced mangoes aside.
For dressing, in a blender container or food processor bowl combine the 1/2 cup chopped mango, vinegar, oil, honey, mint, and chives. Cover and blend or process until smooth. Season to taste with salt and pepper. Drizzle about half the dressing over salad greens; toss gently to coat. Arrange salad on individual plates. Top with mango slices, remaining dressing, and additional freshly ground pepper. Makes 8 to 10 servings.