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In a sauce pot on medium heat, heat 5 cups of milk with 1/4 teaspoon of salt, 1/2 cup of sugar, 1 split vanilla pod, and 2 cinnamon sticks until it's just starting to bubble around the edges, but not boiling.
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Meanwhile, in a large pot, melt 1 tablespoon of butter on medium heat, then add in the arborio rice. Toast the rice in the butter for 1 minute, to open up the kernels.
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Lower the heat to medium-low, then cook for 35-40 minutes, until the rice is tender and the texture of the mixture has become rich and creamy. A good way to tell that the rice pudding is done is dipping a back of a wooden spoon into the mixture, and using your finger to draw a line down the length of the spoon. If it's thick and the line stays separated, that means there's a ton of starch in the mixture, and it should be super creamy.
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When the rice pudding is done, remove the vanilla pod and cinnamon sticks, then pour it into a glass bowl and cover with plastic wrap. Make sure to press the plastic wrap onto the rice pudding, to keep it from forming a skin.
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Refrigerate the rice pudding for at least 4 hours.
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Once the pudding is cooled, stir in the heavy cream, and serve.