Make the filling: In a large bowl, stir the apple slices, lemon juice, granulated sugar, light brown sugar, all-purpose flour, cinnamon and nutmeg together until thoroughly combined.
Cook the filling: Transfer the apple filling to a large skillet or Dutch oven and place over medium-low heat. Stir occasionally and cook for about 10 minutes, or until the apples begin to soften.
Add vanilla: Remove the skillet from the heat and stir in the pure vanilla extract until combined.
Preheat and roll the dough: Preheat your oven to 400°F. On a floured surface, roll out one disc of chilled pie dough (keep the other in the refrigerator). Use gentle pressure with your rolling pin, starting from the center and rolling outward in all directions. Turn the dough as you go, smoothing any cracks around the edges. Lightly flour the surface, rolling pin, and your hands as needed to prevent sticking. Roll the dough into a 12-inch circle.
Line the pie dish: Gently place the rolled-out dough into a 9-inch glass pie dish that is 1.5 to 2 inches deep. Use your fingers to tuck the dough into the dish, ensuring it is smooth and evenly fitted.
Add the filling: Spoon the apple filling into the prepared pie crust, even if it’s still warm from the precooking step. It may look like a lot, but that’s okay—pile the apples high and pack them tightly using your hands. The apples should mound to the same height or slightly higher than the edge of the crust. Pro Tip: Always spoon the filling into the crust rather than pouring it in. This helps you discard any excess liquid at the bottom of the bowl, which can make the crust soggy. The apples will release more moisture as they bake, so removing the extra liquid now ensures a perfect texture.
Finish assembling: Take the second disc of chilled pie dough from the refrigerator and roll it out on a floured surface into a 12-inch circle.
Create the top crust: To make a lattice crust, use a pastry wheel, sharp knife, or pizza cutter to cut the rolled-out dough into 12 strips, each about 1 inch wide. Carefully weave the strips over and under each other to form a lattice pattern, pulling back strips as needed for the woven design. If you prefer not to lattice the crust, simply place the rolled-out dough over the apple filling and cut 4 slits in the top to allow steam to vent.
Trim and seal the edges: Use a small paring knife or kitchen shears to trim any excess dough. Fold the overhanging dough back toward the center of the pie, gently pressing to adhere the top and bottom crusts. Where the two crusts meet, lift and press to seal, then fold the edges under for a neat finish. Rotate the pie plate and repeat this process until all the edges are tucked under. Seal the edges by fluting them with your fingers or pressing them with the back of a fork around the perimeter of the pie.
Brush and sprinkle: Lightly brush the top of the pie crust with egg wash, then sprinkle evenly with coarse sugar to ensure a golden, glossy finish.
Bake the pie: Set the pie on a large baking sheet and bake uncovered for 25 minutes.
Prepare a pie crust shield: Cut a 14-inch square of aluminum foil and fold it in half. On the folded edge, cut out a 5-inch semi-circle. Unfold the foil to create a circular ring to shield the crust.
Adjust temperature and continue baking: After 25 minutes, reduce the oven temperature to 375°F. Carefully place the aluminum foil shield over the edges of the pie crust to prevent over-browning, pressing it gently into place with oven mitts (be cautious, as the pie will be hot!). Leave the center of the pie exposed, and bake for an additional 35–40 minutes, or until the filling is bubbly around the edges. Pro Tip: If the top of the pie begins to brown too quickly, loosely tent the entire pie with foil for the remaining baking time.
Cool the pie: Remove the pie from the oven and place it on a cooling rack. Let it cool for at least 4 hours before slicing and serving to allow the filling to set. Slicing while the pie is still warm can result in a too-juicy filling.
Store leftovers: Cover the pie and keep it at room temperature for up to 1 day, or refrigerate it for up to 5 days.