Roll the dough out and fit into a 9-inch metal pie pan. Fold the edges under and crimp the edges, or just trim the edges if using a tart pan.
Refrigerate the crust while you make the filling and topping.
Filling
Peel and core the apples, then slice 1/4 inch thick.
In a stock pot, toss the apples with the lemon juice, sugar, 4 tbsp flour, and spices. Bring to a simmer over medium heat, then reduce to low. Stirring frequently, simmer the apples for about 15-20 minutes, just until they begin to soften and the juices become syrupy.
Set aside to cool for 30 minutes.
Topping
In a bowl, combine the flour, brown sugar, salt, and spices. Add the melted butter and stir until moistened and crumbly.
Set aside until needed.
Bake
Preheat the oven to 400 F, and position a rack in the lower third of the oven.
Place the pie pan with the chilled crust on a baking sheet lined with parchment paper. Sprinkle the crust with the remaining 1 tbsp flour.
Spread the apple filling into the crust, letting the apples mound up in the center. Bake the pie (without the crumb topping) for 20 minutes at 400 F. Reduce the oven temperature to 375 F, and continue to bake for another 20 minutes.
Remove the pie from the oven, and sprinkle the crumb topping over the apples. If the edges of the pie crust are getting too brown, go ahead and cover them with a pie crust shield, or strips of foil.
Return the pie to the oven and bake at 375 F for another 30-35 minutes, or until the filling is bubbling over the edges and the topping is golden brown.
Set the pie on a cooling rack and cool for several hours. Sprinkle the crumb topping with the ground vanilla.If you want to serve the pie warm, it will be delicious, but a little messy. For neat slices, let the pie cool for 1 hour at room temperature, then chill in the refrigerator for 3 hours to speed up the cooling and to help the filling set.