In a casserole, cook rice in a big quantity of boiling water until tender, about 20 minutes. Drain and set aside.
In another casserole, not on heat, whip egg, sugar and flour until mixture is homogeneous. Add rum, milk and coconut milk. Stir at low heat until it thickens. Remove from the heat and incorporate the cooked rice.
Spread the bland mange (pudding) in individual serving dishes, cover with a plastic wrap and put in fridge.
Caramelized Coconut :
Put parchment paper on a baking sheet. Rinse coconut with hot water in a strainer while shaking it.
In a non-stick skillet, dissolve brown sugar in water.
Add coconut and cook until liquid has evaporated and coconut is golden. Spread coconut on the parchment paper and let cool.
When ready to serve, garnish the cold blanc mange with caramelized coconut.