Preheat oven; roll pie dough and fit into pie plate: Preheat oven to 450°F. On a lightly floured work surface, roll out smaller piece of pâte brisée into a 15-inch round about ⅛-inch thick, dusting surface with flour to prevent sticking, as needed. Brush off excess flour. Roll dough around rolling pin, and place over a deep-dish 9-inch pie plate. Line plate with dough, pressing it into the corners and trim to within 1 inch of the pie plate. Cover with plastic wrap; refrigerate.

Roll out remaining dough and refrigerate: Roll out remaining piece of dough into an 18-inch round. Transfer round to a baking sheet; cover with plastic wrap, and refrigerate.

Make filling: Peel and core apples, and cut into ¼-inch-thick slices. Place slices in a large bowl; sprinkle with lemon juice to prevent discoloration. In a small bowl, combine flour, sugar, and cinnamon; toss with apple slices.

Add filling to pie plate: Remove remaining dough from refrigerator; place apple mixture into prepared pie plate, mounding it in a tall pile. Dot filling with butter.

Place dough over apples and seal: Place dough round over the apples. Tuck edge of top dough between edge of bottom dough and rim of pan. Using your fingers, gently press both layers of dough along the edge to seal, and crimp as desired.

Cut vents; brush with egg and sprinkle with sugar: Using a paring knife, cut several vents in top of dough to allow steam to escape. In a small bowl, whisk together egg yolk with 2 tablespoons water to make a glaze. Brush surface with egg glaze; sprinkle with sugar.

Bake; reduce heat and bake: Place pie plate on a baking sheet and transfer to oven. Bake until crust is golden, about 15 minutes. Reduce oven temperature to 350°F and continue baking until crust is golden brown and juices are bubbling, 1 hour to 1 hour 15 minutes.

Let cool: Remove from oven, and let pie cool completely before serving.