In a large bowl, whisk together the flour, salt, and sugar. Add the cold cubed butter and use a pastry cutter or your fingertips to work it into the flour until pea-sized pieces remain.
Combine the ice water and apple cider vinegar, then drizzle over the flour mixture, stirring with a fork until the dough just begins to come together.
Divide the dough into two portions—approximately ⅔ for the bottom crust and ⅓ for the top. Flatten each portion into a rectangle, wrap tightly in plastic wrap, and refrigerate for at least 30 minutes.
While the dough chills, peel, core, and slice the apples into ¼-inch thick pieces.
In a large bowl, toss the apples with both sugars, cornstarch, spices, salt, lemon juice, and vanilla extract until every slice is evenly coated. Let the mixture sit for 10 minutes.
Preheat your oven to 375°F (190°C). On a lightly floured surface, roll the larger portion of dough into a rectangle approximately 17×12 inches.
Transfer to a 15×10-inch rimmed baking sheet, allowing the excess to hang over the edges.
Pour the apple filling onto the dough and spread evenly, leaving a 1-inch border. If your apples have released excess liquid, use a slotted spoon to transfer them, leaving most of that liquid behind.
Roll out the remaining dough to approximately 15×10 inches. Place it whole on top for a traditional look or cut it into lattice strips for a more decorative appearance.
If using a solid top crust, be sure to cut several vents to allow steam to escape during baking.
Fold the overhanging bottom crust up and over the top crust, pinching to seal.
In a small bowl, whisk together the egg and milk, then brush this egg wash over the entire top crust. Sprinkle with coarse sugar if desired.
Place the slab pie on the middle rack and bake for 45-50 minutes, or until the crust is deeply golden and the filling is bubbling through the vents.
If the edges begin browning too quickly, shield them with aluminum foil after about 30 minutes.
Allow the pie to cool for at least 1 hour before slicing to let the filling set properly.