For the pear pockets, peel the pears, cut them in half and remove the core. Cut the flesh into small cubes. Heat the butter in a frying pan, add the pear cubes and sprinkle with sugar. Cook the pears in the butter for at least 5 minutes, stirring frequently. Remove and let cool completely.
For the short pastry, pile the flour in a baking bowl. Put the butter cut into small pieces in the center, add the egg and incorporate the flour from the edge. Melt the sugar and salt in water, and add this mixture little by little, kneading everything into a smooth dough. Form the dough into a ball, let it rest in the refrigerator for an hour with the lid closed.
Roll out the dough to a thickness of 5 mm, and cut out round dough patties of 8 to 9 cm ø with a glass or cookie cutter. Place a tablespoon of diced pears on one half of the circle, moisten the edges of the dough a little, and fold the empty half over the filling to make crescent-shaped pockets. Place these on a baking sheet and let rest in the refrigerator with the lid closed.
Heat the oil in a deep fryer or large saucepan. gradually add the filled patties to the hot oil and bake until done, about 7 minutes. Remove the pear pockets from the oil with a slotted spoon and drain on kitchen roll. Sprinkle the pastry with powdered sugar and serve to the table while still hot.