In the bowl of your instant pot, place the rice, 2 cups of the milk, plus the cream, sugar, and salt, and stir to combine.
Secure the lid of your instant pot, set the vent to seal, press “manual” and set the time to 6 minutes.
The pot will switch on and come to pressure, then begin counting down the 6 minutes.
Once the timer has sounded to signal the end of the cooking period, turn off the pot and allow the pressure to release naturally by allowing the pot to sit, undisturbed, for about 20 minutes.
Release any remaining pressure manually by turning the venting dial to “vent.”
Open the lid of the pot, and turn the instant pot back on to sauté by pressing the “Sauté” button.
Once the mixture begins to simmer, in a small bowl, whisk the remaining 3 tablespoons of milk and the egg.
Beginning with a very small amount of the simmering rice pudding, temper the egg (slowly raise its temperature so the egg doesn’t scramble) by adding some of the simmering rice pudding to the egg mixture and whisking to combine.
Transfer the egg mixture to the instant pot bowl, and allow to simmer, stirring constantly, until it thickens enough that a spatula along the bottom of the instant pot leaves a visible trail that the mixture takes a moment to fill.
For the stovetop with cooked rice.
In a medium saucepan, place the cooked rice, 1 1/2 cups (12 fluid ounces) milk, sugar, and salt over medium heat.
Cook, stirring frequently until the mixture comes to a simmer and begins to thicken (about 8 minutes).
Place the remaining 1/2 cup milk and the egg in a separate bowl, and whisk to combine well.
Add about 1 cup of the hot milk and rice mixture to milk and egg mixture, a bit at a time, whisking to combine.
Transfer the egg mixture to the saucepan and continue to cook until the pudding has begun to thicken, about 2 to 3 minutes more. Remove the saucepan from the heat, stir in the optional vanilla extract, and mix to combine.
For the stovetop with raw rice.
In a large saucepan, place the water, rice, and salt, stir to combine and bring to a boil over medium heat.
Reduce the heat to a simmer, and cook stirring frequently for about 10 to 15 minutes, or until the rice has absorbed most of the water, leaving behind no more than a bit of thick, starchy water. Be careful not to overcook the rice.
While the rice is cooking, in a separate, medium-size saucepan, combine the milk, sugar, optional whole cinnamon and nutmeg, and cook over medium heat until simmering (about 2 minutes).
Once the rice in the separate saucepan is cooked, pour the simmering milk mixture through a strainer into the larger saucepan.
Discard the whole cinnamon and nutmeg.
Cook the rice and milk mixture over medium-low heat, stirring frequently until the rice has absorbed most of the milk mixture and the entire mixture has thickened and begins to appear pudding-like, about 15 minutes more.
It will thicken as it cools. Add the optional vanilla, and mix to combine.
For all versions.
Add the optional vanilla and mix to combine. Transfer the prepared rice pudding to serving dishes and serve warm with ground cinnamon to taste.
Alternatively, for a firmer pudding, place plastic wrap directly on the surface and allow to cool at room temperature until no longer hot to the touch.
Cover tightly and refrigerate for at least 1 hour before serving chilled with ground cinnamon to taste.