1. Preheat the oven to 375°. With a pastry brush, spread the softened butter evenly over the bottom and sides of a large, shallow baking dish about 14 inches long, 8 or 9 inches wide and 1˝ to 2 inches deep.
2. If you are using vanilla beans, cut them lengthwise into halves with a small, sharp knife. Then, using the tip of a spoon, scoop out the tiny black seeds and set them aside.
3. There should be about ˝ teaspoon of seeds. (Place the pods in a 1-quart jar, fill it with 2 pounds of sugar, and cover tightly. Within 2 or 3 days the sugar will be vanilla-flavored; use it for any dessert purpose you like.)
4. Put the pineapple, mango, papaya and bananas through the coarsest blade of a meat grinder. Transfer the fruit pulp and its liquid to a sieve set over a deep bowl and stir until all the liquid has drained through.
5. Measure 1 cup of it and combine it with the arrowroot in another bowl. Mix thoroughly. Then stir the arrowroot mixture into the fruit puree and add the remaining liquid, the brown sugar and vanilla seeds (or extract).
6. Transfer the mixture to the buttered baking dish, spreading it out evenly with a spatula. Bake in the middle of the oven for 1 hour, or until the top is golden brown.
7. Cool to room temperature, cover with plastic wrap and refrigerate for at least 4 hours, or until thoroughly chilled.
8. Serve the poe directly from the baking dish and present the coconut top milk separately in a bowl.
