Preheat oven to 375°F (190°C).
Roll out bottom pie crust and place into a 9-inch pie dish.
In a large bowl, mix apples, granulated sugar, brown sugar, flour, cinnamon, nutmeg, lemon juice, and salt.
Spoon apple mixture evenly into pie crust.
Drizzle half of the salted caramel sauce over apples.
Dot top with small cubes of butter.
Cover with top crust and seal edges, then cut small slits for steam.
Brush crust with beaten egg.
Bake for 50–55 minutes until crust is golden and filling is bubbly.
Cool for at least 1 hour before slicing.
Drizzle remaining salted caramel over slices before serving.