To make pastry, place flour and salt in bowl of food processor. Pulse to combine. Add butter and pulse just until mixture resembles coarse crumbs with some pea-size pieces of butter remaining; do not over mix. In measuring cup, whisk egg yolk with vinegar then add enough ice water to bring mixture to 1/4 cup (60 mL). Gradually pour yolk mixture through feeder tube in top of food processor while pulsing to form a crumbly dough. Transfer to lightly floured surface and pat into 2 disks (pastry will still be crumbly; do not knead). Wrap each disk in plastic. Chill 1 hr.
Meanwhile, in large bowl make the filling by tossing the sliced apples with the sugar, flour, cinnamon and lemon juice. Set aside.
Preheat oven to 220°C (425°F). Roll 1 pastry disk on a lightly floured surface to 1/8-in. (3 mm) thickness. Line bottom, sides and rim of a deep dish 9-in. (23 cm) pie plate. Prick bottom with a fork a few times. Spread apple filling in pie shell, mounding in centre. Dot with the pieces of butter.
Whisk the egg with 1 tbsp (15 mL) water to make an eggwash; brush onto edges of the pie shell. Roll second pastry disk into 1/8-in. (3 mm) 12-in. (30 cm) round. Drape over filling. Press top and bottom edges together. Trim pastry. Crimp edges with fingers or press with tines of a fork. Brush pastry with eggwash. Use a sharp knife to cut 2 vent holes in the top.
Bake pie on lowest rack 20 min. then reduce temperature to 180°C (350°F) and bake another 50 min. to 1 hr., or until pie crust is golden brown and juices are bubbling. Transfer to a wire rack to cool completely. Serve with Cheddar cheese, if desired.