While making the filling, prepare the pie dough according to the recipe and refrigerate. Set the oven to 425°F.
In a medium saucepan set over medium heat, melt the butter. Add 3 tablespoons of flour and stir continuously while simmering for 1 minute. Bring to a boil while whisking in ¼ cup water and 1 cup sugar. Reduce heat, simmer for an additional three minutes while whisking regularly, and then turn off the heat.
Seven cups of apples, peeled, cored, and thinly sliced, should be put in a big basin. 1 ½ teaspoons of cinnamon should be sprinkled over the top and combined. After adding the sauce to the apples, toss them to evenly distribute the coating.
Roll out the bottom pie crust to a circle of 12" in diameter after flouring your work surface. Transferring it to the 9" pie plate requires wrapping it around your rolling pin. A tiny mound should be created in the center of the apple mixture before adding it. Avoid getting filling on the edges as this will make it difficult to seal.
Using a pizza cutter, roll the second crust into an 11" round and cut it into 10 evenly sized strips. Over the top, arrange the strips in a woven lattice pattern (see video tutorial). Brush the top with the egg mixture, which you'll have beaten with 1 Tbsp. water.
For 15 minutes, bake in the center of a 425°F oven. Bake for an additional 45 minutes, or until the apples are tender and the filling is bubbling through the vents, after lowering the heat to 350 F. * Before serving, rest at room temperature for an hour.