Bring two cups of water to a boil. Stir in rice and reduce heat to Low. Simmer for 20 minutes, covered, stirring occasionally until the water is absorbed.
Stir half-and-half, brown sugar, cinnamon, and salt into the cooked rice. Cook on medium heat, stirring frequently to prevent sticking and clumping. Continue for about 15 minutes, until thick and creamy.
Stir in egg, skim milk, and raisins and cook for another 5 minutes.
Remove from heat and stir in butter and vanilla extract.