Caramel Apple Pie

Make the Salted Caramel:

Place 3/4 cup granulated sugar and 1/4 cup water in a medium, heavy-bottomed saucepan over medium-high heat. Stir with a wooden spoon until the sugar is dissolved, then stop stirring and bring to a boil. Meanwhile, measure out 1 cup heavy cream, 2 tablespoons unsalted butter, and 1/2 teaspoon kosher salt.
Continue to boil, swirling the pan occasionally but not stirring, until it turns a dark-amber color (380ºF to 390ºF). This will take anywhere from 5 to 10 minutes, depending on your pan and stove. There will be pale yellow streaks, then darker ones will appear. When you see these, pick up the pan with the handles and swirl occasionally, and be attentive.
Remove the pan from the heat. While whisking continuously, immediately but slowly pour in the cream. Be very careful — it will steam and bubble up violently! It may also ball up or clump, but just keep whisking until smooth again. Add the butter and salt and whisk until smooth.
Return the pan to medium-low heat and simmer until slightly thickened and reduced to about 1 1/4 cups, 4 to 5 minutes. Transfer to a heatproof bowl or container and let cool for at least 1 hour before using (it will thicken more as it cools). Meanwhile, prepare the crusts.
Prepare the Crusts:

Arrange a rack in the middle of the oven and heat the oven to 375°F. Roll out 1 pie dough on a lightly floured work surface into a 12-inch-wide round about 1/8-inch thick. Transfer into a regular 9-inch pie plate (not deep dish). Press the dough into the plate, but do not trim the edges. Refrigerate.
Roll out the second pie dough into an 11-inch-wide round. Place on a sheet of parchment paper. Cut into 3/4-inch-wide strips. Slide the parchment onto a rimmed baking sheet and refrigerate.
Assemble and Bake the Pie:

Place 1 large egg yolk and 1 tablespoon water in a small bowl and whisk with a fork until combined.
Place 1/2 cup packed dark brown sugar, 1/4 cup all-purpose flour, 1 teaspoon ground cinnamon, 1/2 teaspoon kosher salt, and 1/4 teaspoon ground nutmeg in a large bowl and stir to combine, breaking up any clumps of sugar.
Peel 2 1/2 pounds Granny Smith or Pink Lady apples. Halve and core the apples, then cut into 1/4-inch-thick slices. Add to the bowl of spiced sugar and toss to combine, making sure there are no clumps of sugar or flour left in the bottom of the bowl.
Pour the spiced apples into the crust, slightly mounding the apples in the center. Drizzle with 1/2 cup of the salted caramel sauce.
Create a lattice pattern with the pie dough strips: Lay half the strips horizontally over the apples, using the longer strips in the middle and the shorter strips toward the edges. Space the strips evenly apart (about 3/4-inch). Fold every other strip back on itself about halfway.
Lay one of the longer remaining pie strips vertically over the apples so that it lays across the unfolded horizontal strips in the center. Swap the folded and unfolded horizontal strips: Unfold the folded horizontal strips so they lay over the vertical strip, and fold the strips running under the vertical strip back over top.
Lay another vertical strip of pie crust over the apples. Continue swapping the folded and unfolded horizontal strips and adding one new vertical strip each time. Continue until one half of the pie is completely latticed.
Lattice the second half of the pie following the same pattern. If the strips start to soften too much while you’re creating the lattice, refrigerate the pie and dough strips for about 5 minutes before continuing.
Trim the edges with kitchen shears if needed, then roll the edges inwards toward the center of the pie. Firmly crimp the edges to seal. Place the pie on the now-empty parchment-lined baking sheet. Brush the lattice and edges with the very thin layer of the egg wash. Sprinkle the lattice with 1 tablespoon coarse sugar if desired.
Bake until the crust is golden-brown and the filling is bubbling around the edges, 50 to 60 minutes. Check 40 minutes into baking: If the crust starts to brown too quickly, loosely cover the pie with aluminum foil and continue baking.
Transfer the pie to a wire rack and let cool for at least 2 hours before slicing. Serve slices with the remaining caramel sauce.