In a medium bowl, whisk together lime juice, oil, scallions, honey, salt and cayenne until well blended. Add mango and papaya and toss gently.
Wash avocados, then halve lengthwise and remove pits. With a small spoon, scoop out avocado meat in large pieces; reserve shells. Cut avocado into 1/2" cubes.
Add avocado and cheese to the bowl and toss very gently to combine.
Mound salad into avocado shells and place on 4 serving plates. Spoon excess salad along side. If using greens, arrange next to avocados and spoon excess salad on top.