Peel the prawns, leaving the tails intact, then rinse and pat dry. Put all the dressing ingredients into a small bowl and whisk to mix.
Up to 1 hr before serving, peel and stone the avocados, then cut into thick slices and put in a large bowl with half the dressing. Mix lightly to coat all the slices (this prevents them turning brown). Chop the basil and add to the bowl along with the prawns. Toss everything together lightly. Scatter the leaves over a platter, then spoon the prawns, avocado and basil mix over. Drizzle with the remaining dressing and serve with lime wedges for squeezing over.