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.
In a clean saucepan, combine cooked rice, 1-1/2 cups milk, sugar, and salt. Cook over medium heat until thick and creamy, 15 to 20 minutes.
Slowly stir in remaining 1/2 cup milk, beaten egg, and raisins. Cook 2 minutes more, stirring constantly.
Remove from heat and stir in butter and vanilla.