Make your pie dough and shape it into two discs. Wrap them well and chill for at least 2 hours. Cold dough is far easier to roll and keeps the crust flaky.
If you are making your own caramel, do it now so it can cool. Store-bought caramel works too if you want a shortcut. Just warm it gently before using so it pours easily.
Add the sliced apples, sugar, lemon juice, flour, and spices to a large bowl. Stir until every slice is coated evenly. The mixture should look glossy and smell amazing.
Flour your counter and roll one chilled disc into a 12-inch circle. Ease it into the pie dish and smooth it against the sides. Keep the second disc in the fridge until you need it.
Spoon the apples into the crust and pile them high, packing them tightly. Drizzle 1/2 cup (145g) of caramel over the top. If it has thickened, warm it for a few seconds first.
Roll the second disc into a 12 to 14-inch circle and cut about 18 strips, each 1/2 to 3/4 inch wide. Weave them over the filling, then trim the extra dough. Fold the edges inward, pinch them together, and crimp.
Whisk the egg and milk, then brush it over the lattice and edges. Sprinkle on coarse sugar if you like. Chill the pie for 20 to 30 minutes while the oven heats to 400°F (204°C).
Place the pie on a baking sheet and bake at 400°F for 25 minutes. Lower the oven to 375°F (190°C), add a crust shield, and bake 35 to 40 minutes more. The filling should bubble and reach about 200°F (93°C).
Let the pie cool on a rack for at least 3 hours. This step is not optional, because the filling needs time to set. Drizzle the remaining caramel over the whole pie or onto each slice.