In a food processor, add 1 and ½ cups of flour, salt, and sugar. Pulse until combined, It should only take a few pulses.
Add in all the cubed butter and turn the processor on high. Let it mix until the butter is in pea-sized pieces. This will take about a minute.
Add in the rest of the flour and pulse 5 - 10 times to mix the flour well.
Dump the flour mixture into a bowl and add the cheddar cheese. Stir to combine.
Add in 6 tablespoons of water. Mix with a spoon thoroughly. If you pinch the dough and it stays together, it's ready! If you pinch the dough and it falls apart, add 1 to 2 more tablespoons of water.
Turn the crust out onto a clean workspace and knead it until the dough has formed into a ball. When you first put it on the workspace, it will fall apart and be crumbly. It will come together.
Split the dough into two pieces and form them into discs. Cover them with plastic wrap and place them in the fridge for about 1 hour.
After the hour is up, take one disc out of the fridge and put on a floured surface. Flour the top of the dough and rolling pin also.
Roll out into a circle. You'll want it to be about 12 inches.
Fold the dough in half and pick it up and place onto the pie plate. Unfold the dough and push the dough onto the bottom and sides.
Trim the edges. I cut them even with the edge of the pie plate using a knife. Set aside.
In the large bowl of sliced apples, add in the cinnamon and nutmeg. Stir until the spices are evenly distributed.
Pour the apple slices into the pie crust. Set aside.
In a medium saucepan, add in the butter. Place over medium heat and let the butter melt completely.
Add in the flour and cornstarch. Stir until the flour and cornstarch are both incorporated.
Add in the apple cider/juice, granulated sugar, brown sugar, and salt. Stir to combine. Let the mixture come up to a boil and boil for 1 minute. Reduce heat and simmer for another minute.
Stir in the vanilla extract.
Pour the mixture on top of the apples. You can reserve about ⅓ of the mixture to brush on the top of the pie crust if you want it to resemble mine. I would just pour it on top of the apples.
Repeat the rolling out with the top piece of dough.
In a small bowl, crack the egg and beat it. Using a pastry brush, rub the egg wash onto the bottom edge of the pie crust.
Lay the top layer of dough on. Cut some steam holes into the top layer. You can cut the steam holes before you place the dough on the pie or after.
With your forefinger and thumb, crimp the pie crust together. I usually form a "U" with my forefinger and thumb on the inside of the edge. With my other forefinger, I push the dough between my thumb and forefinger resting on the inside. (I hope this helps)
With the pastry brush, cover the top layer with the egg wash.
If you're brushing the rest of the sugar syrup on the top of the pie crust, do this now.
Place into the at 425 degrees for 15 minutes and then turn the heat down to 350 and bake another 50 minutes.