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In a food processor, pulse the flour, cheese and salt to mix. Add the butter and pulse until the mixture resembles coarse meal. Transfer the mixture to a large bowl and make a well in the center. Stir in the eggs and work the dough into a ball.
Divide the dough into quarters and flatten into disks. Roll out each disk to an 11-inch round between 2 sheets of wax paper. Remove the wax paper and line two 9-inch pie pans with a dough round. Refrigerate the lined pans and the 2 dough rounds, covered, until thoroughly chilled.
Preheat the oven to 375°. In a large bowl, toss the apples with the lemon juice. Sprinkle on the brown sugar, flour and salt and toss well. Divide the apples between the lined pie pans. Moisten the pie-shell rims and cover with the dough rounds. Trim any overhang and crimp the edges to seal. Cut 4 steam vents in each pie.
Bake the pies on the bottom shelf of the oven for about 1 hour, or until golden and bubbly and the apples are tender when pierced; cover the pies with foil halfway through if necessary. Let cool for about 1 hour before serving.