Combine the rice and water in a pot and bring to a boil.
Once a boil is reached, reduce the heat as low as it will go to maintain a slight simmer, and cover the pot until the rice absorbs all the liquid. This takes about 31 minutes.
Add the Splenda, salt, and 1 1/2 C of skim milk, and increase the heat to medium low.
While stirring frequently, cook the rice and milk mixture until it thickens (about 24 minutes).
Add the egg to the remaining milk, and then slowly add that mixture to the pot while stirring constantly.
Cook for an additional 3-4 minutes, until the rice thickens further but still has some moisture. Essentially, at this stage you’re looking for a consistency that’s a bit soupier than rice pudding normally is, because the custard will set as it cools and reach normal rice pudding consistency. Cooking it too far at this stage will result in a very dense rice pudding once it sets.
Once the above consistency is reached, remove the pot from the heat and add the remaining ingredients, mixing thoroughly. Serve the rice pudding warm or cold.