Heat oven to 350 degrees F. Grease a 1-quart oven-proof casserole dish.
Bring the 1 cup water to a boil in a large saucepan. As soon as the water boils,
add the salt and the rice. Cover and cook over low heat for 15 minutes or until
all the water is absorbed.
Pour in the milk and simmer for 5 to 10 minutes, just until the milk comes to
a boil. Remove the pan from the heat and stir in the vanilla extract.
In a small, heavy-bottom frying pan, melt the butter over medium heat. Add the
cream and the brown sugar. Bring to a boil, reduce the heat to low, and simmer for
2 minutes, stirring constantly. Pour the cream mixture into the rice. Stir well.
Spoon this into the casserole dish.
Bake for 20 minutes or until the pudding is thick and has a golden crust.