Apple Pie with Cheddar Cheese

Name: Apple Pie with Cheddar Cheese
Cuisine: American
Ingredients: 2 recipes Pie Dough, made with lard; 2 recipes Pie Dough, made with lard; 9 cups sliced apples, such as Greening, Cortland, Winesap, or other hard cooking apples (8 to 10 apples); 9 cups sliced apples, such as Greening, Cortland, Winesap, or other hard cooking apples (8 to 10 apples); 9 cups sliced apples, such as Greening, Cortland, Winesap, or other hard cooking apples (8 to 10 apples); 9 cups sliced apples, such as Greening, Cortland, Winesap, or other hard cooking apples (8 to 10 apples); Juice of 1 lemon; ⅓ cup sugar; ½ teaspoon cinnamon; 1½ teaspoons quick cooking tapioca (if apples are very juicy); 1½ teaspoons quick cooking tapioca (if apples are very juicy); 3 tablespoons unsalted butter, cut into bits; 1 egg yolk beaten with 2 tablespoons cold water, for egg wash; 1 egg yolk beaten with 2 tablespoons cold water, for egg wash; 1 egg yolk beaten with 2 tablespoons cold water, for egg wash; Cheddar cheese, sliced