Peel, core, and slice apples. Toss with lemon juice, both sugars, cinnamon, nutmeg, and salt in a large bowl. 

In a large skillet or saucepan over medium heat, melt the butter and add the apples. Cover and cook for 3 minutes. 

Place cornstarch in a large bowl. Slowly whisk the water (or apple juice) into the cornstarch. Once combined, add to apples. Continue cooking for an additional 5 minutes, stirring frequently, until apples are fork tender and sauce is thickened. (*Add more water/juice, if needed, for desired sauce consistency.) 

Cool the apple pie filling to at least room temperature before using for the pie.

Combine flour and salt in a large bowl. Stir. Cut in shortening with a pastry blender, two forks, or pulse in a food processor until pea-sized chunks are achieved. 

Add the egg, vinegar, and 5 Tbsp of ice-cold water. Mix with your hands. Add more water 1 Tbsp at a time until the mixture comes together in a ball. Empty the contents from the bowl onto a floured surface.

Cut dough in half and flatten each half into a flat disc. Wrap the discs with plastic wrap, and place them in the freezer for 15 minutes. (Pie Crust Tutorial HERE.)

Once the dough has chilled, remove one piece at a time. Flour your surface and rolling pin. Roll dough from the center outwards, rotating and adding extra flour as needed until 1/8-inch thin.

Carefully transfer the dough to the standard 9-inch pie dish. Shape the crust to the bottom and sides of the pie dish. Trim excess crust.

Fill the pie shell with the cooled apple pie filling. Roll out the second half of the pie dough for the top. (Cut out designs if desired [i.e. leaves] and set aside.) Lightly brush the edges of the bottom pie crust with a whisked egg (egg wash). Lay the top pie crust over the apples. Trim, seal, and crimp the edges.

Cut slits in the top of the pie crust (if you didn't cut out any designs). Brush the top and edges of the crust with egg wash. (Attach the designs now, if desired.) Combine 1 tsp of cinnamon and 2 Tbsp granulated/coarse sugar. Sprinkle generously over the pie crust.  

Bake in a preheated 350 degrees Fahrenheit oven for 1 hour + until the filling is bubbling in the center and the crust has browned. If crust browns before filling bubbles, cover the pie with foil and continue baking. Cool pie to room temperature before slicing and serving.