Make the Pie Crust: In a large bowl, whisk together the flour and salt. Cut in the cold butter using a pastry blender or your fingers until the mixture resembles coarse crumbs. Gradually add the ice water, one tablespoon at a time, mixing until the dough just comes together. Form the dough into a disc, wrap it in plastic wrap, and refrigerate for at least 30 minutes.

Prepare the Apple Filling: In a large bowl, combine the sliced apples, granulated sugar, flour, cinnamon, nutmeg, and lemon juice. Toss gently to coat all the apple slices evenly. Melt the 2 tablespoons of butter in a large skillet over medium heat. Add the apple mixture and cook for about 5-7 minutes, stirring occasionally, until the apples are slightly softened.

Brown the Butter for the Crumble Topping: Place the butter in a light-colored saucepan over medium heat. Cook, swirling occasionally, until the butter melts, foams, and then turns a golden-brown color with a nutty aroma. Be careful not to burn it! Remove from heat and let cool slightly.

Make the Crumble Topping: In a medium bowl, combine the flour, brown sugar, and salt. Pour in the browned butter and stir until the mixture forms coarse crumbs. Stir in the rolled oats.

Assemble the Pie: Preheat oven to 375°F (190°C). On a lightly floured surface, roll out the pie crust into a 12-inch circle. Carefully transfer the crust to a 9-inch pie plate. Trim and crimp the edges of the crust.

Fill and Top the Pie: Pour the apple filling into the prepared pie crust. Sprinkle the crumble topping evenly over the apples.

Bake the Pie: Bake for 45-55 minutes, or until the crust is golden brown and the filling is bubbly. If the crust starts to brown too quickly, cover the edges with foil or use a pie shield.

Cool and Serve: Let the pie cool completely on a wire rack before slicing and serving.