Bring water to a boil in a large, heavy saucepan. Stir in the salt and rice. Cover and simmer over low heat, stirring once or twice, until the water is almost fully absorbed, 15-20 minutes.

Add milk, cream and sugar. Increase heat to medium-high and bring to a simmer. Reduce heat to maintain a low simmer.

Cook, uncovered, and stirring frequently until mixture starts to thicken, about 30 minutes.

Reduce heat to low and continue to cook, stirring every few minutes to prevent scorching, until spoon is just able to stand up in the pudding (~ 15 minutes longer.

Remove from heat and stir in the vanilla. Cool and serve chilled or at room temperature. To store, press plastic wrap directly on surface and refrigerate for up to 2 days.