This is a best-seller at the Elsens' pie shop—and once you see how good lightly spiced apples taste when they're bathed in homemade caramel, you'll know why. (Note: You can make the pie crust ahead of time.)
Use a bench scraper to cut butter into ½-inch cubes. (If butter begins to "sweat," dust with flour.) In a large, flat-bottomed bowl, combine flour, sugar, and salt. Add the butter cubes and toss to coat with the flour mixture. Use a pastry blender to cut the butter into the flour; do not smash or smear the butter. Scrape butter off the pastry blender during the mixing process and continue mixing. (If butter is softening too fast, put the bowl in the refrigerator until butter firms up, 2–5 minutes.) Continue cutting, working quickly, until butter is broken down and looks like a coarse crumble with only a few larger pieces.
Combine vinegar with water and ice; you’ll use 10–12 tablespoons of this liquid in the pie dough. Begin by sprinkling 4 tablespoons of liquid over the flour mixture; use a bench scraper or your hands to incorporate until the mixture begins to come together. Sprinkle in 4 more tablespoons of liquid and continue the mixing process. Squeeze a fistful of dough: if it holds, like wet sand, it’s ready. If it falls apart, add 1–2 more tablespoons of liquid at a time, squeezing the dough to check if it holds. Bring all the dough together, sprinkling dry bits with more small drops of liquid as necessary; dough will look shaggy. Knead in the bowl just until incorporated.
Turn dough onto a work surface and use a bench scraper to divide dough into two equal pieces. Shape into flat disks and wrap in plastic. Refrigerate for at least 30 minutes, preferably overnight. (Note: dough can be refrigerated for up to 3 days and frozen up to 1 month, tightly wrapped.)
Generously grease pie dish with softened butter. Dust a work surface and a rolling pin with flour. Place one chilled pie disk on the work surface and lightly dust it with flour. (Keep the other disk refrigerated until it's time to make the lattice top in Step 6.) Roll dough by starting at the center and lightly pressing down with the rolling pin to flatten slightly. Rotate the dough and repeat, pressing down so it’s evenly flattened all around, about ⅛-inch thick. Then roll outward to make a circle, rotating the dough a quarter-turn at a time to keep it even. (If dough is softening too fast, chill in the refrigerator until firm, 2–5 minutes.) Roll the dough until it's about 2–3 inches larger than the pie dish, all the way around.
Overturn pie dish onto the center of the dough circle, and use a pizza wheel to trim away the rough edges. (Save the scraps to make crust cookies!) Remove the pie dish and place it right side up on your work surface. Use the light indentation created by the rim as a guide for gently positioning dough into the center of the dish. (If dough is softening too fast, put it back into the refrigerator until it firms up, 2–5 minutes.) Fit crust gently into dish, being careful not to stretch the dough. Begin crimping the edge by using your fingers to roll the dough firmly so it rests on top of the rim. Crimp by using your index finger and thumb on one hand to squeeze a letter “C” into the dough rim. (Lightly flour your fingers if the dough is sticking.) Repeat, crimping the entire pie and making sure the final fluted crust sits directly on top of the pan’s rim. Place in refrigerator for at least 15 minutes to let the dough set again before adding the filling.
Lattice: Dust a clean surface with flour. Roll out second chilled dough disk to a circle slightly larger than the pie dish, between ⅛- and ¼-inch thick. Using a pizza wheel, trim rough edges from left and right sides to square them off. Cut the dough into 8 strips of equal width. Transfer strips to a baking sheet and refrigerate, 30 minutes.
Apples: Prepare the apples using an apple peeling machine or peel, core, and thinly slice with a sharp knife or mandoline. Place in a bowl and toss with lemon juice and sugar. Set apples aside to soften slightly and release juices, 20–30 minutes.
Caramel Sauce: Whisk sugar and water together in a medium saucepan, and cook over medium-low heat until the sugar is just dissolved. Add the butter and bring to a slow boil. Continue stirring over medium heat until the mixture turns a deep, golden brown color, almost copper. Turn off heat and immediately but slowly add the heavy cream (use caution, as the mixture may bubble up rapidly). Whisk the final mixture well to combine; set aside to cool while you prepare the pie filling. Makes about 2 cups. (Caramel Sauce can be made several days in advance. Cool, then store in the refrigerator in an airtight container; bring to room temperature before using.)
Filling: Preheat oven to 425 degrees F. In a small bowl, add the bitters to the raw sugar and mix with your fingers to combine. Add salt, cinnamon, nutmeg, allspice, black pepper, and flour; mix well. Leaving behind excess liquid, add prepared apples to the sugar spice mixture. Gently toss the apples to coat.
Assembly: Tightly pack the apples into the chilled pie shell, mounding the apples slightly higher in the center. Spread ½ cup Caramel Sauce evenly over the apples with a spatula (use more sauce if you’d like a sweeter pie). Sprinkle with flaky sea salt.
Lattice top: Assign a number to each strip of dough: 1 being the longest and 8 being the shortest. Lay strip 1 across the top of the pie, just slightly to the left of center. Lay strip 2 over strip 1 at a 90-degree angle, just below the center of the pie. Lay strip 3 over strip 2, to the right of and parallel to strip 1. Lay strip 4 over strip 2, to the left of and parallel to strip 1. Fold back the right end of strip 2 so it’s on top of strip 5; fold back the top ends of strips 1 and 5 and lay strip 6 above and parallel to strip 2. Return the top ends of strips 1 and 5 to their original positions. Fold back the bottoms of strips 1 and 5 and lay strip 7 below and parallel to strip 2. Return the bottom ends of strips 1 and 5 to their original positions. Fold back the top ends of strips 3 and 4 and lay strip 8 above and parallel to strip 6. Return strips 3 and 4 to their original positions.
Trim the lattice edges so they're flush with the edge of the pan. Roll and pinch the bottom crust overhang inward to build up the crust edge. Crimp the edge of the pie all the way around so that the final fluted crust sits directly on top of the pan's rim. Brush the crust with the egg wash, being careful not to smudge the caramel (it will burn as the pie bakes). Sprinkle with raw sugar and flaky sea salt. Pie will bake for a total of 50–55 minutes. Place the pie on a rimmed baking sheet on the lowest rack of the preheated oven. Bake until crust is set and beginning to brown, 20 minutes. Lower the oven temperature to 375 degrees F, move the pie to the center oven rack, and continue to bake until the pastry is a deep golden brown and the juices are bubbling, 30–35 minutes longer.
Test the apples for doneness with a skewer or sharp knife; they should be tender and offer only the slightest resistance. Cool completely on a wire rack, at least 2 hours. Serve slightly warm or at room temperature.