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Bring a medium saucepan of water to a boil. Add the salt and rice and cook over moderately high heat, stirring occasionally, until the rice is barely tender, about 10 minutes. Pour the rice into a colander to drain it.
In the same saucepan used to boil the rice, combine the cream, milk and sugar and bring to a boil. Stir in the rice, lemon zest, cinnamon stick and vanilla and simmer over low heat, stirring often, until the rice is tender and the mixture is thick, about 45 minutes. Remove and discard the cinnamon stick and lemon zest.
In a small bowl, beat the egg yolks with 1/2 cup of the hot rice. Remove the rice pudding from the heat and stir in the yolk mixture. Scrape the pudding into a large heatproof bowl and blend in the butter. Let cool to room temperature, stirring often. Sprinkle with cinnamon and serve at room temperature or chilled.
The rice pudding can be refrigerated overnight.