Using a food processor, add flour, brown sugar and salt; pulse until well combined.

Cut butter into small cubes. Add butter and shredded cheese to the food processor; pulse until a crumbly mixture forms (~10 pulses).

Add water; pulse until well combined. If necessary, add 1-2 more Tbsp of water at a time (and pulsinuntil dough comes together in a ball.

Divide dough into 3 equal pieces. Shape each piece into a disc and wrap with plastic wrap; refrigerate for at least 1 hour. (Note: Dough can be made the day before and refrigerated overnight.)

Preheat oven to 425°F.

Using a large bowl, add sliced apples, sugars, lemon juice, flour, cinnamon, nutmeg and salt; stir until well combined.

Working on a well-floured surface, roll one piece of pie dough into an 11” circle.

Press dough into bottom and sides of a 9” pie dish. Spread apple mixture into an even layer on top of the dough. Dot top of filling with small cubes of butter.

Brush edges of the dough with the beaten egg; set pie dish aside.

Roll remaining piece of dough into a 9” circle. Using a small square (or rouncontainer, cut squares out of the pie dough. Lay the dough on top of apple filling.

Roll the remaining piece of pie dough out into a large circle. Using the small container, cut more squares out of the dough. Reroll any scraps and continue cutting until all dough has been used.

Lay the squares around the edges of the pie to create the crust. (Tip: Brush a little bit of the egg wash onto each square to help the squares stick together.)

Brush top of pie with the remaining beaten egg. Sprinkle top of pie generously with turbinado or another coarse sugar.

Set pie pan on parchment-lined baking sheet. Bake at 425°F for 20 minutes.

Reduce oven temperature to 375°F and continue baking for 20 minutes. Tent pie with foil to prevent the top from burning and continue baking for 20-25 minutes, or until apples are soft.

Transfer pie to a cooling rack and let cool for at least 1½ hours before slicing.