Pour water into a saucepan and bring to a boil over medium heat.

Once boiling, stir in rice and reduce to low heat. Cover and simmer until rice is tender and water is absorbed, approximately 20 minutes. 

Using a clean saucepan, combine rice, 1-1/2 cups of milk, sugar, and salt. Cook over medium heat and stir often until thick and creamy, about 15 minutes. 

Stir in remaining milk, egg, and raisins. Cook for 2 more minutes, stirring constantly before removing from heat.

Stir in butter and vanilla until combined. 

Serve warm.