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 make mixture equal 1/4 cup (60 mL). With food processor running, pour in egg mixture then pulse just until crumbly dough starts to form. Transfer to lightly floured surface and pat into 2 disks (dough will still be crumbly; do not knead). Wrap each in plastic wrap and chill 1 hr.
Meanwhile, to make filling, toss apples with the sugar, flour, cinnamon, lemon juice and butter. Set aside.
Preheat oven to 425°F (220°C). Roll one of the pastry disks on a lightly floured surface to approx. 1/4-in. (5-mm) thickness. Line bottom and sides of a deep-dish, 9-in. (23-cm) pie plate. Scrape filling into pie shell, mounding in centre. Whisk egg with 1 tbsp (15 mL) water and brush edge of the pie shell. Roll remaining pastry disk into a 12-in. (30-cm) round and drape over filling. Press to seal the two pieces of pastry together. With a paring knife, trim pastry to edge of pie plate.
Seal the two crusts by crimping the edge with a thumb and forefinger or a fork. Brush top crust with egg wash and cut vent holes in centre. Bake on lowest rack 20 min. then reduce temperature to 350°F (180°C) and bake another 50 to 60 min., or until piecrust is golden brown and juices are bubbling. Transfer to a wire rack to cool completely. Serve with Cheddar cheese, if desired.
Pie dough can be made 24 hr. in advance, wrapped and refrigerated.