Preheat the Oven: Preheat the oven to 180°C/350°F.
Grease the Baking Dish: Generously grease a 10-cup or larger casserole dish with the unsalted butter.
Warm the Milk Mixture: Add the milk, white sugar, and vanilla extract to a saucepan over medium-high heat. Stir until the sugar dissolves and continue heating until the surface becomes foamy and the milk reaches a simmer; do not let it boil, as the milk may split. Combine the Rice Mixture: Place the uncooked medium-grain rice, sultanas or raisins, and cinnamon in the prepared casserole dish.
Add the Warm Milk: Pour the hot milk mixture over the rice, dried fruit, and cinnamon, then briefly stir everything together.
Cover the Dish: Cover the casserole dish securely with its lid or aluminum foil before placing it in the oven.
Bake the Pudding: Bake for 1 hour, stirring every 20 minutes to loosen the rice from the base and prevent it from setting there.
Stir in the Cream: Remove the pudding from the oven after 1 hour and stir in the cream thoroughly. The pudding may appear somewhat watery immediately after baking, but the excess liquid evaporates quickly. Check the Texture: Keep the pudding creamy and loose enough to gently ooze when served, rather than allowing it to become overly thick.
Serve Warm: Serve the rice pudding immediately on its own, or add a scoop of vanilla ice cream for a richer dessert.