Bring the rice, butter, and water to a boil in a large saucepan over high heat. Reduce heat to medium-low, cover, and simmer until the rice is tender, and the liquid has been absorbed, 20 to 25 minutes.
Whisk together 2 cups of milk, flour, sugar, egg, and vanilla extract in a bowl, and pour the milk mixture over the cooked rice. Stir to combine, and simmer over low heat for 15 minutes. Stir in 1 cup whole milk, the cream, raisins, and cinnamon until thoroughly mixed, and allow to cool for a few minutes. Serve warm or cold.
