Position a rack in the center of the oven and heat the oven to 425°F.Melt the butter in a 12-inch skillet over medium heat. Add the apple slices and cook, stirring often, until softened, about 4 minutes.
Sprinkle 1 Tbs. of the sugar, the cinnamon, and 1/4 tsp. salt over the apples; cook, stirring often, for 1 minute more. Remove from the heat.
In a small bowl, beat the egg with 2 Tbs. of water. Lightly brush the edges of each pastry rectangle with some of the egg wash. Spread the cooked apples and any juice over half of the long side of each rectangle, but not over the egg wash border. Fold the pastry half without apples over the side with apples, long side to long side. Press to seal the edges tightly and transfer to a large rimmed baking sheet.
Brush the tops with some of the remaining egg wash and sprinkle each with 1/4 tsp. of the remaining sugar.
Bake until puffed and golden, about 16 minutes. Serve warm.
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