Cook the rice: In a medium saucepan, bring the water and rice to a boil. Reduce heat to low, cover, and simmer for 15 minutes, or until the rice is tender and water is absorbed.
Add the milk and cream: Stir in the milk, cream, sugar, and salt. Cook over medium-low heat, stirring frequently to prevent sticking.
Simmer until creamy: Continue cooking for about 20 minutes, stirring often, until the pudding thickens and the rice is very soft.
Optional egg yolk step: If using, whisk the egg yolk in a small bowl. Stir in a spoonful of the hot pudding mixture to temper it, then slowly mix it back into the pot and cook for 1–2 more minutes.
Stir in vanilla: Once the pudding is creamy and thickened, remove from heat and stir in the vanilla extract.
Let it rest: Let the pudding sit for 5–10 minutes to thicken slightly as it cools.
Serve and garnish: Scoop into bowls and sprinkle generously with cinnamon. Serve warm or chill before enjoying.