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Preheat the oven to 425 degrees Fahrenheit.
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Combine sugar, flour, and lemon zest in a saucepan; stir together until thoroughly blended.
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Add cider vinegar while stirring or whisking constantly; add the water.
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Place over medium heat; bring the mixture to a boil and cook, stirring constantly, for 1 minute.
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Remove from heat and stir a little of the hot mixture into the eggs; stir the warmed egg mixture into the remaining hot mixture.
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Stir in the butter.
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Pour the mixture into the prepared pie shell.
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Bake for 10 minutes at 425 degrees Fahrenheit.
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Reduce heat to 350 degrees Fahrenheit.
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Continue baking for 30 minutes more.
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Remove the pie from the oven and let it cool completely before serving.
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(The filling will seem quite liquid, but will firm as the pie cools.)
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This pie has pretty much the same ingredients as the one above, but the method is different and therefore you end up with a slightly different pie.