In a medium saucepan, combine 1 1/2 cups water and rice over high heat. Bring to a boil, reduce heat, cover and simmer for 45 minutes.
In another saucepan, combine 1 1/2 cups cooked rice, 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 raisins. Cook 2 minutes more, stirring constantly. Remove from heat, and stir in butter and vanilla. Serve warm.