Preheat the oven at 350°F (180°C).
Peel, core and cut apples into approximately ¼-inch slices.
Roll out the cold pie dough on a lightly floured surface and have two large pieces of parchment paper and a baking sheet ready.
Halfway through rolling, transfer the pie crust circle to the paper and continue rolling until ¼ to ⅛ inch thick.
Put the paper on the baking sheet, place another piece of paper on top (to avoid dryness), and refrigerate it while you prepare the filling.
Mix apple slices with cinnamon and sugar in a small bowl and combine lightly, until the apples are coated but be careful not to break them.
Leaving about 2-inch border (up to 3 inches top) of dough on the outer edge, put the apple slices over the dough, making mounds or concentric circles until the surface is covered. If the apples released liquid, strain it before using the apples. Don't discard it.
Sprinkle the apples with the chopped nuts.
Lift the sides of the dough inward, covering part of the apples and exposing the center.
Mix the egg with a tablespoon of water and brush the folded edges with a pastry brush. Sprinkle with some extra brown sugar.
If you have some reserved liquid from the apples, drizzle it now on top of the apples.
Bake immediately for about 40 minutes, until the apples are soft and the crust is golden and fully baked.
Let cool on a wire rack for about 10 minutes and carefully lift it, transferring the paper to the cooling rack to cool down more.
Serve warm with caramel sauce or dulce de leche and a dollop of ice cream or whipped cream.
Store leftovers at room temperature for a day or in the refrigerator for a few days, always covered in plastic wrap or a container.