In a medium saucepan, combine the cooked rice, 2 cups of milk, sugar, salt, and cinnamon.
Cook over medium heat, stirring often, until the mixture thickens—about 15–20 minutes.
In a small bowl, whisk the egg with the remaining 1/2 cup milk.
Slowly stir the egg mixture into the pot. Keep stirring so the egg doesn’t scramble.
Cook for another 5 minutes, stirring constantly, until creamy.
Remove from heat and stir in the vanilla. Add raisins or fruit if using.
Serve warm with a little sprinkle of cinnamon on top.