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In a deep saucepan (at least 3 quart size) add the water and salt and bring to a boil.
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Add rice to boiling salted water, cover, and cook over low heat until moisture is absorbed and rice is fluffy.
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Add milk and sugar and cook 25 minutes.
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Remove from heat.
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In a small bowl beat eggs well until light.
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Dissolve cornstarch in 2 Tblsp. milk mixture.
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Add dissolved cornstarch to well beaten eggs and blend thoroughly.
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Slowly pour egg mixture into milk mixture, stirring constantly until well blended.
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Simmer over low heat for 2 minutes, stirring constantly to prevent curdling. Mixture will be slightly thickened.
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Remove from heat and stir in vanilla.
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Pour into individual dishes.
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Sprinkle with cinnamon.
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Serve warm or refrigerate.