In a large bowl, whisk together the flour and salt. Cut in the cold butter using a pastry blender or your fingers until the mixture resembles coarse crumbs. Gradually add the ice water, one tablespoon at a time, mixing until the dough just comes together. Divide the dough in half, flatten each half into a disc, wrap in plastic wrap, and refrigerate for at least 30 minutes.

In a large bowl, combine the sliced apples, sugar, flour, cinnamon, nutmeg, and lemon juice. Toss gently to coat all the apple slices evenly. Set aside.

In a medium saucepan over medium heat, melt the sugar, stirring constantly with a wooden spoon or heatproof spatula. The sugar will first clump up, then melt into a clear amber liquid. Continue cooking until the sugar turns a deep amber color. Be careful not to burn it. Remove from heat and immediately add the butter, stirring until melted and smooth. Slowly pour in the heavy cream (it will bubble up!), then add the salt. Stir until the caramel sauce is smooth and creamy. Let cool slightly.

Preheat oven to 375°F (190°C). On a lightly floured surface, roll out one disc of dough into a 12-inch circle. Carefully transfer the dough to a 9-inch pie plate. Trim and crimp the edges. Pour the apple filling into the pie crust. Pour about half of the caramel sauce evenly over the apples.

Roll out the second disc of dough and either place it over the pie as a top crust, cutting slits for venting, or cut it into strips to make a lattice top. If using a full top crust, brush with egg wash (if using) to promote browning.

Bake for 45-55 minutes, or until the crust is golden brown and the filling is bubbly. If the crust starts to brown too quickly, cover the edges with foil. Let the pie cool completely on a wire rack before serving. This is important so the filling can set up. Drizzle the remaining caramel sauce over the pie before serving.