Preheat your oven to 375°F (190°C). If using a homemade pie crust, roll it out to fit a 9-inch pie dish. Press the crust into the dish, crimping the edges decoratively. Dust the bottom with 1 tablespoon of flour.
In a large bowl, combine the sliced apples, granulated sugar, flour, cinnamon, nutmeg, and allspice. Sprinkle with lemon juice and vanilla extract, then toss until all apple slices are evenly coated. Let the mixture sit for 10 minutes.
In a medium bowl, combine flour, brown sugar, and cinnamon. Add the cold, cubed butter and use a pastry cutter, two forks, or your fingertips to work the mixture until it resembles coarse crumbs with pea-sized butter pieces. If using, fold in the oats and chopped nuts.
Pour the apple filling into the prepared pie crust, mounding slightly in the center. Sprinkle the crumb topping evenly over the apples, covering the entire surface. Place the pie on a baking sheet to catch any potential bubble-overs.
Bake in the preheated oven for 50-55 minutes, or until the crumb topping is golden brown and the apple filling is bubbling around the edges. If the edges of the crust begin to brown too quickly, shield them with aluminum foil or a pie crust shield.
Remove the pie from the oven and place it on a wire cooling rack. Allow it to cool completely for at least 2 hours before slicing.