Prepare the Pie Crust: In a mixing bowl, whisk together 1 ¼ cups all-purpose flour and ½ tsp salt. Grate ½ cup frozen butter into the flour mixture, allowing the butter to be evenly distributed. Add 4-5 tbsp chilled water and ½ tsp cider vinegar, mixing until a dough forms. Shape it into a disk, wrap in plastic, and chill in the refrigerator for at least 2 hours.
Preheat the Oven: Set your oven to 375°F (190°C). While the oven is heating, roll the dough out on a floured surface until it's about ¼ inch thick. Carefully place the dough in a pie plate, trimming any excess. Pre-bake the crust with weights for 15 minutes, then remove the weights, prick the bottom with a fork, and bake for an additional 10-15 minutes until slightly golden.
Make the Crumble Topping: In a medium bowl, combine 7 tbsp melted butter, ⅔ cup brown sugar, ½ tsp cinnamon, ⅛ tsp nutmeg, and 1 cup all-purpose flour. Stir until the mixture resembles coarse crumbs. Chill until ready to use.
Prepare the Apple Filling: In a saucepan over medium heat, melt ½ cup butter and add ¼ cup water. Stir in 3 tbsp flour, followed by ¼ cup granulated sugar, ¼ cup brown sugar, and 1 ½ tsp cinnamon. Add 2 ½ lbs Granny Smith and Pink Lady apples that have been cored and sliced. Cook for about 3 minutes until the apples soften slightly.
Assemble the Pie: Pour the apple filling into the pre-baked crust, ensuring that the apples are evenly distributed. Sprinkle the chilled crumble topping generously over the apples.
Baking the Pie: Bake the assembled pie in the preheated oven for 50-55 minutes, or until the topping is golden brown and the filling is bubbling. Allow the pie to cool for at least 30 minutes before slicing.