Whisk together 1 1/4 cups flour and 1/2 tsp salt in a large bowl, then cut in the cold cubed butter using a pastry cutter until the mixture resembles coarse crumbs with pea-sized butter pieces. Add ice water one tablespoon at a time, stirring gently with a fork, until the dough just barely comes together when squeezed.
Turn the dough out onto a lightly floured surface, press it into a flat disc, and wrap tightly in plastic wrap. Refrigerate for at least 30 minutes, or up to 2 days.
Peel, core, and slice apples to 1/4-inch thickness and place in a large bowl. Add both sugars, flour, cinnamon, nutmeg, allspice, lemon juice, and vanilla extract, then toss until all apple slices are evenly coated. Set aside to rest while you prepare the streusel and crust.
Whisk together the flour, brown sugar, cinnamon, and salt in a medium bowl, then cut in the cold cubed butter until the mixture forms coarse, clumpy crumbs. Stir in the rolled oats, then refrigerate the streusel until ready to use.
Preheat the oven to 375 degrees F (190 degrees C) and place a rimmed baking sheet on the lowest rack to catch drips. Let the chilled dough sit at room temperature for 5 minutes before rolling.
Roll the dough on a lightly floured surface into a 12-inch circle, then carefully transfer it into the 9-inch pie pan and press it into the bottom and sides. Trim the overhang to 1/2 inch, fold it under itself along the rim, and crimp the edges decoratively. Refrigerate for 10 minutes.
Spoon the apple filling into the chilled unbaked crust, piling it generously, and pour any accumulated liquid from the bowl over the top. Sprinkle the chilled streusel evenly over the entire filling, pressing it into loose clumps for better texture.
Cover the crust edges with foil or a pie shield and bake for 25 minutes, then remove the shield and continue baking for 25-30 more minutes, until the streusel is deep golden brown and the filling is visibly bubbling. Total bake time is 50-55 minutes.
Transfer the pie to a cooling rack and let it cool for at least 2 hours before slicing, allowing the filling to set completely. Serve warm or at room temperature with vanilla ice cream or whipped cream.