In a small bowl, combine the raisins and rum. Set aside.
Combine the rice and salt with 1 1/2 cups water in a medium heavy-bottomed stainless steel saucepan. Bring it to a boil, stir once, and simmer, covered, on the lowest heat for 8 to 9 minutes, until most of the water is absorbed. (If your stove is very hot, pull the pan halfway off the burner.)
Stir in 4 cups of half-and-half and sugar and bring to a boil. Simmer uncovered for 25 minutes, until the rice is very soft. Stir often, particularly toward the end. Slowly stir in the beaten egg and continue to cook for 1 minute. Off the heat, add the remaining cup of half-and-half, the vanilla, and the raisins with any remaining rum. Stir well.
Pour into a bowl, and place a piece of plastic wrap directly on top of the pudding to prevent a skin from forming.
