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Special Equipment: 9-inch cake pan or molds
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Preheat the oven to 350 degrees F.
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Caramel: In a heavy-bottomed pan, bring the sugar and water to a boil over medium heat Stir with a wooden spoon, until a pale brown color develops.
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Remove from the heat, and let rest for 2 to 3 minutes, then pour into the cake pan, evenly coating the entire bottom.
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The caramel is extremely hot, so be careful when pouring it into the cake pan or molds.
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In a saucepan over medium-high heat, add the condensed milk, the milk, the lime juice and zest, orange liqueur, and vanilla.
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Simmer for 12 to 15 minutes, stirring throughout to combine flavors.
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In a mixing bowl, whisk the eggs and yolk together, then slowly temper into the milk mixture, constantly stirring the eggs into the warmed milk.
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Slowly incorporating the eggs will keep the eggs from scrambling.
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Pour milk mixture over the caramel in cake pan.
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Put the cake pan into a larger shallow vessel filled halfway up with water.
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Put the dish into the oven and bake for 40 to 50 minutes.
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Remove the flan from oven and let cool.
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Refrigerate the flan overnight.
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To remove the flan from the pan, put the pan into a shallow container with about 1-inch of warm water.
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Let sit for about 10 minutes, which will soften the caramel and make it easier to remove.
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Invert the flan onto a platter and serve.