Bring 1 1/2 cups water to a boil in a saucepan; stir rice into boiling water. Reduce heat to low, cover, and simmer for 20 minutes.
After 20 minutes, stir in 1 1/2 cups milk, sugar, and salt. Cook over medium heat until thick and creamy, 15 to 20 minutes. Stir in remaining 1/2 cup milk, beaten egg, and cinnamon; cook two minutes more, stirring constantly. Remove from heat and stir in butter and vanilla.
Place almond/raisin/etc. in one bowl. Spoon portions rice pudding into all bowls. Mix up all the bowls until the location of the special bowl is unknown. Serve hot or cold.