Preheat the oven to 375 degrees F. Line baking sheets with parchment.
Lightly flour your work surface. Unfold 1 puff pastry sheet at a time and roll each into a 10 by 15-inch rectangle. Using a ruler, cut each into 2 (5 by 15-inch) rectangles, then cut each rectangle into 5 (5 by 3-inch) rectangles. Transfer the 20 rectangles on to the baking sheet and chill in the fridge until cold.
Peel, halve and core the pears, and then cut them into 1/4-inch thick slices. Toss them with the almonds, cherries, sugar, cornstarch, salt, lemon juice and almond extract.
Remove the rectangles from the fridge, place 5 of them on a new baking sheet and evenly spoon half the fruit mixture onto them, leaving a little bit of a border all around. Beat the egg and lightly brush the borders. Lay 5 more rectangles of dough over the filling. Use a fork to press them gently sealed. Repeat with the remaining dough and filling. Refrigerate for 20 minutes.
Brush the tops with the beaten egg. Cut 3 vents, about 1/2-inch long, in the top of each pie. Sprinkle with sugar. Bake, rotating once, until the crust is golden and you see the juices bubbling, 25 to 30 minutes. Cool the pies on a cooling rack at least 20 minutes before serving.
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