Put 1 tablespoon of lime juice, 1 teaspoon of rum or Planteur and a hazelnut-sized piece of butter in each of the 4 halves. Sprinkle the edge of each papaya half with 1 tablespoon of cane sugar and add 1 tablespoon of it to the lime juice, rum and butter mixture in the papaya half (otherwise it will be too sour). Place half a split vanilla pod in the papaya.
Place the papayas in a lightly buttered casserole dish and bake in the preheated oven for about 20 minutes.
Then remove the vanilla pods and pour coconut milk into the halves. Serve hot or warm.
I think this recipe is particularly good because I really like the (but very unknown) mixture of lime with coconut. The recipe comes from Martinique.