Make the Pie Dough:

1. In a large bowl, combine flour and salt.
2. Cut in cold butter using a pastry cutter or food processor until mixture resembles coarse crumbs.
3. Add ice water gradually until dough comes together. Divide in two, flatten into disks, wrap, and chill for 30 minutes.

Make the Caramel Sauce:

1. In a saucepan over medium heat, melt the sugar while stirring constantly until it turns golden brown.
2.  Add the butter (careful—it will bubble) and stir until melted.
3. Slowly add cream, stir until smooth, then add salt and vanilla. Let cool.

Prepare the Apple Filling:

1. Toss sliced apples with sugar, cinnamon, nutmeg, lemon juice, and cornstarch. Let sit for 15–20 minutes. Drain excess liquid.

Assemble the Pie:

1. Roll out one dough disk and place in a 9-inch pie plate. Fill with apple mixture, layering and drizzling caramel between.
2. Roll out the second dough disk and cut into strips for a lattice crust. Weave on top and seal edges.
3. Brush top with egg wash (egg + milk).

Bake the Pie:

1.  Preheat oven to 400°F (204°C). Bake for 20 minutes.
2.  Lower heat to 350°F (177°C) and continue baking for 35–40 minutes until golden brown and bubbling.
3. Cool for at least 3 hours before slicing.