In a small saucepan bring the water to a boil. Add the rice and a pinch of salt. Simmer it, covered, for 15 to 20 minutes until all of the water is absorbed. Fluff with a fork. Transfer the rice to a bowl and let cool.

Preheat the oven to 300 degrees. Butter a 9 inch shallow baking dish.

Bring the milk and heavy cream to a boil in a pan. Scrape the vanilla bean seeds in.

In another bowl, whisk together the eggs, yolks, honey, sugar, salt, rum, and orange zest until well combined. Add the rice.

Add the milk mixture to the bowl in a slow stream while whisking. Pour it all into the baking dish.

Put the baking dish inside a larger pan. Add hot water until it reaches halfway up the side of the pan. Bake the rice pudding for one hour or until it is set.

Let the rice pudding cool and then chill it, covered in plastic wrap, for at least 6 hours or overnight in the fridge.

Just before you are ready to serve it, cover the top with the brown sugar. Try to spread the sugar evenly over the top. Do a better job than I did.

Broil the sugar 2 to 3 minutes until it is melted. It is easy to burn the sugar, so keep your eye on it. When the sugar is browned and shiny, serve your baked rice pudding.