In a large mixing bowl, combine 2 ½ cups of all-purpose flour, 1 teaspoon of salt, and 1 tablespoon of granulated sugar. Cut in 1 cup of cold butter until the mixture resembles coarse crumbs. Gradually add 6 to 8 tablespoons of ice-cold water, mixing just until the dough comes together. Divide the dough into two halves, wrap them in plastic wrap, and refrigerate for 30 minutes.

Peel and slice 6 to 7 medium apples, preferably Granny Smith or Honeycrisp, and place them in a large bowl. Toss the apples with ½ cup of granulated sugar, 2 tablespoons of brown sugar, 1 teaspoon of cinnamon, ¼ teaspoon of nutmeg, 1 tablespoon of lemon juice, 2 tablespoons of flour or cornstarch, and 1 teaspoon of vanilla extract.

Preheat your oven to 375°F (190°C). Roll out one portion of the chilled dough on a floured surface until it fits a 9-inch pie dish. Gently place the rolled dough into the dish and fill it with the well-mixed apple filling. Roll out the second dough portion, drape it over the filling, and seal the edges by crimping. Make slits in the top crust to allow steam to escape.

Place the assembled pie in the preheated oven and bake for 45 to 50 minutes until the crust is golden and the filling bubbles through the slits. If edges brown too quickly, cover with foil.

Once baked, remove the pie from the oven and allow it to cool at room temperature for at least 1 hour to help the filling set.