1. Preheat oven to 400°F (200°C).
2. Prepare a 9-inch pie dish with one pie crust.
3. Peel, core, and slice apples into 1/4 to 1/2-inch thick slices.
4. Toss apple slices with lemon juice, granulated sugar, brown sugar, flour, cinnamon, and nutmeg in a large bowl.
5. Optionally, cook the apple mixture on the stove over medium heat for 5 minutes to enhance flavor.
6. Pour apple filling into the prepared pie crust and spread evenly.
7. Dot the filling with small pieces of butter.
8. Place the second pie crust on top, either as a full crust or a lattice design.
9. Seal the edges and crimp them for a decorative finish.
10. Brush the top crust with an egg wash and sprinkle with coarse sugar.
11. Use a pie shield or foil to cover the crust edges to prevent over-browning.
12. Bake at 400°F for 25 minutes, then reduce temperature to 375°F and bake for another 30-35 minutes.
13. Check if the internal temperature reaches 195°F for doneness.
14. Let the pie cool for at least 2 hours before slicing.
15. Serve warm or at room temperature with vanilla ice cream, whipped cream, or caramel sauce.
16. Store at room temperature for up to 2 days or refrigerate for a few more days.
17. Optionally, freeze the unbaked pie for later use.