Cheddar cheese and apples make a delicious savory and sweet combination. Martha made this recipe on episode 706 of Martha Bakes.
Preheat oven to 425 degrees, with rack in lowest position. On a lightly floured work surface, roll out the smaller disk of dough just under 1/4 inch thick on a lightly floured surface and fit into a 9-inch glass pie plate. Roll remaining disk to just under 1/4 inch thick and transfer to a parchment-lined baking sheet for top crust; refrigerate along with pie plate.
Place lemon juice in a large bowl. Peel, quarter, and core apples; thinly slice crosswise, tossing with lemon juice as you work. Add sugar, flour, cinnamon, and salt to bowl; toss to combine.
Fill bottom crust with apple mixture; lightly brush edge of crust with water. Using a paring knife, cut out either a circle or small slits in center of top crust. Place top crust over filling; press all around edge to seal with bottom crust. Using kitchen shears, trim to a 1-inch overhang; fold dough under itself to form a rim, and press to seal. Using thumb and forefinger, crimp as desired.
Place pie plate on a parchment-lined rimmed baking sheet. Combine lightly beaten egg with 1 tablespoon water. Brush crust with egg wash. Bake 20 minutes; reduce heat to 375 degrees, and bake until crust is golden brown and juices are bubbling, about 80 minutes more. Let cool completely on a wire rack, at least 4 hours (or up to overnight) before serving.