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Preheat oven to 450°F.
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Melt 2 tablespoons of butter in the microwave or in a saucepan.
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In a medium-sized bowl, crack the eggs.
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Beat the eggs lightly and then add the melted butter.
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Measure milk, 1 tablespoon sugar, vanilla, 1/4 teaspoon ground cinnamon, salt, and flour, and add them to the eggs.
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Mix all of the ingredients until the batter is well blended.
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If you have one, use an apple peeler/corer/slicer to peel, core, and slice your apples. If not, use a vegetable peeler to peel the apples.
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Cut out the cores and slice the apples thinly.
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Heat the remaining 3 tablespoons butter in a 10" ovenproof skillet. Add the sliced apples and cook until they are golden brown, 5-10 minutes. (If you'd like, you can add a dash or two of ground cinnamon.)
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Put on oven mitts and take the skillet off the heat. Pour the batter over the apples.
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Measure 2 tablespoons granulated sugar and 1 teaspoon cinnamon and stir them together in a small bowl. Sprinkle the cinnamon sugar over the batter.
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Place the skillet into the oven and cook for 15-25 minutes until gently browned and puffed. (Do not open the oven during the first 15 minutes of the cooking process, or the puff will deflate!)
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Put on oven mitts, remove the skillet from the oven, and immediately place an oven mitt over the handle, so that you won't accidentally burn your hand.
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Cut the puff into wedges and serve immediately.