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Preheat the oven to 350°. Spread the pecans on a rimmed baking sheet and bake for 7 minutes, or until lightly toasted. Transfer to a plate and let cool. Reduce the oven temperature to 325°.
In a large nonstick skillet, melt 4 tablespoons of the butter with the sugar over high heat. Add the apples and cook, stirring frequently, until browned, 12 to 14 minutes. Add the Calvados and cook until evaporated. Let cool.
In a large bowl, combine the brown sugar with the corn syrup, flour and the cooled melted butter and beat until smooth. Beat in the eggs and vanilla.
Spoon the caramelized apples into the Pâte Brisée Pie Shells and pour the custard on top. Scatter the pecans on the custard, lightly pressing them in. Bake in the lower third of the oven for about 1 hour, or until the crusts are golden and the custard is set. Cover the crusts loosely with foil if they brown too quickly. Let the pies cool on a wire rack before cutting into wedges.
The pies can be refrigerated overnight. Bring to room temperature before serving.