- In a large saucepan, cook the rice in plenty of boiling water until tender, about 20 minutes. Drain and set aside.
- In a saucepan, off the heat, whisk together the egg, sugar and flour until the mixture is smooth. Add the rum and milk. Stir over low heat until it thickens. Remove from the heat and stir in the cooked rice.
- Divide the pudding among bowls, cover with plastic wrap and refrigerate.
- Line a baking sheet with parchment paper. Rinse the coconut under hot water while shaking in a colander.
- In a non-stick skillet, dissolve the brown sugar in the water. Add the coconut and cook until the liquid has evaporated and the coconut is golden brown. Spread the coconut on the parchment paper and let cool.
- Before serving, garnish the cooled pudding with caramelized coconut.