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After soaking, bring the rice mixture to a boil on high heat, uncovered. When it starts to boil (about 5 minutes), lower the heat to medium and cook for 10 to 12 more minutes or until water is almost evaporated.
While rice is cooking, beat the egg in a bowl. Add the milk and stir well to mix. Add the egg mixture, vanilla extract and condensed milk to the rice and cook over medium-low heat, stirring carefully, until it thickens slightly or until desired consistency, about 25 to 35 minutes.
Let cool uncovered.
Note: be aware that as the rice cools it thickens. The finished product will be thinner than traditional rice pudding.