Rice Pudding

I had a rice craving a few nights ago, but it passed and I was left with some leftover rice.  I decided to make rice pudding.  I've made it before, using recipes where you cook rice in milk, but I wanted a recipe that started with leftover rice.  A quick search of the internet led me to this recipe, which is seemingly very popular based on the rating and number of reviews.
In the recipe, the rice is cooked in water and then cooked in milk.  I used my leftover rice instead, and cooked it in a mixture of milk and half and half (I ran out of milk).  It's pretty rich, with equal parts milk and half and half.  I added Splenda instead of sugar when it was almost done.  (It's kind of silly not to use sugar, given how much half and half is in there, but oh well.)  It seemed like nothing happened for a while and then all of a sudden it thickened rapidly. At that point I had to start stirring it more frequently.  At the very end, a mixture of beaten egg and milk is added and the mixture is cooked for 2 minutes and then removed from the heat.  Vanilla, butter and raisin are added and the pudding is allowed to cool.  I left out the butter since there was already enough butterfat in there, and used yellow raisins since that's what I had.  I put a piece of saran wrap over the top to prevent a skin from forming, and then let it cool in the fridge.  The pudding was very creamy and rich when warm, and was even better when cool.   It didn't have the grainy texture it gets when the rice is cooked in milk.  It was most tasty and I will be making it again, although I probably won't use as much half and half.