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1
To make the rice pudding. Bring about 3 cups of water and the salt to a boil in a medium to large saucepan. Stir the rice and boil for 10 minutes. Drain, and rinse out the pan.
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2
Put the milk and sugar in the pan and bring to a boil. Stir in the rice, reduce the heat to medium/medium-low, and cook at a steady simmer, stirring frequently. Pay particular attention at the beginning, because the milk has a tendency to bubble up exuberantly and will bubble over even in a tall pot if you don't catch it and stir it down in time. Stir in the vanilla at the end.
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3
To make the apples. Cut the apples into 1/4 inch thick slices and then cut each piece crosswise. Sprinkle the sugar in the center of a medium nonstick skillet. Moisten with a splash of lemon juice and then turn the heat to medium high. When the sugar melts, bubbles and start to color, either tilt the pan or stir the sugar with a fork or wooden spoon. As soon as the sugar is a nice amber color, pull the pan away from the heat. Stand away, because the mixture will splatter, and add the butter, swirling to mix it inches.
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4
Put the skillet on medium heat, pour in the cider, and add the salt. Bring the cider to a boil, then add the apples. cook, stirring often for 5 minutes, or until the apples are tender. Pour in the heavy cream and boil for 1 minute more, then turn the apples and caramel sauce into a heatproof bowl and allow to cool. The apples are ready to serve when they are just slightly warm or at room temperature. (Don't taste them as soon as they're cooked: the caramel is very hot.).
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5
Put a little of the caramel sauce in the bottom of each bowl or glass (Martini glasses look great), top with rice pudding, and finish with apples and a little more sauce. If you'd like, add a dollop of whipped cream.
