For the pastry:
Lightly spray a quarter sheet baking rimmed baking pan, about 12-½” x 9”. Preheat the oven to 375-degrees.
Cut the butter into cubes and freeze along with the shortening for about 30 minutes. Combine the flour, kosher salt, and sugar in a food processor and process for about 5 to 10 seconds.
Cut the shortening into pieces and scatter along with the butter cubes on top of the flour mixture and pulse about 10 times, or until the pieces are the size of peas.
Add the cold water and process for about 10 to 15 seconds, just until the pastry dough starts to come together. The pastry dough will still be crumbly in appearance. Don’t over process or your pastry will be tough.
Turn the mixture out on a lightly floured sheet of parchment paper. Gently pull the dough together using the parchment paper, pressing it into a disc. Set aside about ⅓ of the dough for the top crust.
Roll the dough into a rectangle, measuring about 14” x 11” x ⅛” thick, turning occasionally and dusting with flour as needed, so the dough doesn’t stick to the paper. Roll up around your rolling pin and gently place it into a rimmed baking sheet, fitting the dough into the corners and up the edge of the pan. Chill while you prep the apples.
For the apples:
Melt the butter in a large sauté pan over medium heat. Add the apples and cook stirring occasionally until soft, about 5 to 7 minutes.
Add the mascarpone cheese, stirring until the cheese is melted.
In a small bowl whisk the brown sugar with the flour and the spices.
Stir the sugar, spices, and flour into the apples and continue cooking for an additional 3 minutes.
Remove the apples from the heat and add the vanilla extract, and check for seasoning, adding more kosher salt of brown sugar to suit your taste. Set aside to cool while you roll out the top crust.
To assemble:
Roll out the pastry for the top crust, into a large rectangle, about 14” x 10”.
Pile the apples into the pastry shell spreading them evenly.
Lift the pastry for the top crust and place it over the apples.
Turn the edges of the pastry together and tuck under then crimp with a fork, sealing the edges together.
Whisk the egg with the half and half. Lightly brush the top of the pie with the egg wash and sprinkle the extra sugar over the top of the pastry.
Using a sharp knife cut 1” slits across the top of the pastry to allow the steam to escape while the pie bakes.
Bake in a 375-degree oven for about 45 minutes or until the pastry is golden brown in color.
Set the pie on a wire rack to cool before slicing, allowing the juices to set.