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Preheat the oven to 400 degrees. Generously butter six 8-ounce ramekins. Set aside on a rimmed baking sheet.
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In the work bowl of a food processor fitted with the metal blade, pulse the peaches until coarsely chopped. (The pieces should be no large than1/4 inch in size.) Remove 3/4 cup of the chopped peaches and place 2 tablespoons of them in each of the prepared ramekins. Set aside.
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Add the lemon juice, vanilla extract, and a pinch of salt to the remaining chopped peaches in the bowl of the food processor. Process until very smooth and pureed. Transfer 1 cup of the peach puree to a bowl, discarding any remainder or reserve for another use, such as an ice cream topping or base for a smoothie. Set aside.
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In the bowl of a heavy-duty mixer fitted with the whisk, beat the egg whites with a pinch of the salt on medium speed until foamy. Add about 1 tablespoon of the granulated sugar and beat on high speed until the whites hold soft peaks, 1 to 2 minutes. Slowly add the remaining granulated sugar and beat on high speed until the whites are glossy and hold stiff peaks when the whisk is lifted.
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Add about a quarter of the beaten egg whites to the peach puree mixture and stir until well mixed. Pour this mixture over the remaining egg whites and fold them together as lightly as possible.
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Spoon the mixture into the prepared souffles ramekins (the mixture should come up to the top of each). Smooth the top with a metal spatula. Run your thumb around the inside of the rim of each dish, making a shallow channel around the edge of the batter. (This will help the souffles rise up straight and tall.) Set the filled souffles ramekins on the rimmed baking sheet.
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Bake until puffed, golden, and gently set in the center, 8 to 10 minutes. Remove from the oven, sprinkle with confectioners' sugar, and serve immediately.
