To make the pie crust, combine the flour, sugar and salt a large bowl. Cut the butter into the mixture using a pastry blender, two knives, or your hands, until mostly pea-size butter pieces remain. (A few larger pieces of butter are OK!)
Combine the water, ice, and apple cider vinegar in a small bowl. Add the water mixture a few tablespoons at a time, using your hands to bring the scraps together in between, until dough forms a ball. (It’s OK if there are a few dry bits remaining.) Divide into 2 discs, wrap in plastic and chill 1 hour or up to 3 days.
Butter a 9-inch pie pan. (I used a ceramic dish, which worked great.)
On a floured surface, roll out one disc a couple of inches wider than your pan. Place in the bottom of pan, allowing sides to overlap rim by 1 to 1 1/2 inches. Fold and pinch the excess dough inward (no need to perfectly crimp the sides here – you’ll finish this when you assemble the pie.) Roll out remaining pie dough and, using a pizza wheel, cut into 8 strips. Place the strips on a parchment-covered baking sheet. Cover the pie crusts and strips with plastic wrap and place in the refrigerator for at least 30 minutes.
To prepare the salted caramel, cook sugar and water together over low heat until just dissolved. Add the butter and bring to a slow boil. Continue cooking at a low boil (stirring continuously) until mixture turns a deep, golden brown color. Be careful not to burn caramel—remove from heat before it smokes or turns very dark. Remove from the heat and immediately add heavy cream, stirring constantly. The mixture will bubble and steam–be careful as sugar will be very hot. Whisk mixture together over low heat and sprinkle in sea salt. Let cool completely. (NOTE: This makes much more than you’ll need for the pie. Stored in a tightly sealed jar, the caramel will keep for several weeks in the refrigerator.
To prepare the apple filling, sqeeze the lemon juice into a large bowl. Core, peel and thinly slice the apples (the Elsens recommend a mixture of sweet and tart apples, such as Crispin, Granny Smith, and Cortland) and add to the bowl of lemon juice. Toss the apples to coat in lemon juice, and sprinkle with 2 tablespoons sugar. Let sit for 20-30 minutes, so the apples soften and release some of their juices.
Combine the remaining ingredients (raw sugar through flour) in a large bowl. Drain the apples and add to the sugar-spice mixture, tossing gently to combine.
Preheat your oven to 400F.
Remove the pie crust and lattice pieces from the refrigerator. Sprinkle one teaspoon each of flour and sugar in the bottom of the pie crust (this will help prevent the crust from getting soggy while baking). Tightly layer the apples in the pan so that there are minimal gaps, mounding slightly in the middle. (NOTE: The original recipe says to add 1/2 cup caramel sauce here. You can either add it to the pie, or wait and drizzle it on the pie after you bake it. I did the latter, but either option is delicious!).
Arrange the pastry strips in a lattice pattern over the apples. Using your thumb on one hand, and the thumb plus index fingers on your other hand, crimp the edges of crust, incorporating the strips of dough. Place the pie in the refrigerator for 10 to 15 minutes to set the pastry.
Brush the pastry top with an egg wash (1 egg beaten with 1 teaspoon water and a pinch of sea salt) and lightly sprinkle the pie with raw sugar.
Place pie on a baking sheet and bake 20 to 25 minutes, until the pastry is set and beginning to turn brown. Reduce the oven temperature to 375F and continue baking 30 to 35 minutes longer. Test doneness of apples with a long toothpick or small knife. They should be just soft. Let cool at least 1 hour before slicing.
MAKE AHEAD: This pie is quite time-consuming, so I’d recommend making your pie crust dough and caramel sauce the day before. On the day of, just roll out your dough and prepare the apple filling while the pastry is chilling. Dividing this process in half, makes this pie SO much more doable.
NOTE: As I mentioned in the recipe, the caramel sauce can be added to the pie before baking, or drizzled on afterward. You really can’t go wrong…