If using wooden skewers, soak them for 30 minutes before cooking.
In a small bowl, mix together the coconut milk, lime zest and juice, the finely chopped lime leaves, ginger, chilli and fish sauce. Set aside.
Use a sharp knife to slice down the back of each prawn and rinse out the vein.
Thread each prawn with a whole lime leaf on the back onto a wooden or metal skewer. Place in a shallow baking dish and pour half the marinade over. Refrigerate for up to 4 hours before grilling.
To make the papaya salsa, mix the papaya, chilli and mint together in a small bowl and set aside.
Preheat an outdoor grill or chargrill pan. Grill the prawns, lime leaf down, over direct heat for about 3–5 minutes or until they turn pink and are charred at the edges.
Serve the prawns with the remaining marinade, papaya salsa and lime wedges. You could also cook steamed rice to bulk this up.