In a medium saucepan, mix the cooked rice, 1 1/2 cups of the milk, sugar and salt. Cook over medium heat, stirring occasionally, for 15 to 20 minutes until thick and creamy. Stir in the remaining 1/2 cup of milk, raisins, and the beaten egg. Cook for 2 more minutes, stirring constantly. Remove from heat. Stir in the butter and vanilla and sprinkle with cinnamon (optional). This pudding can be stored in the fridge, but it is best served immediately while warm.