In a medium bowl, combine the 1 cup flour, ½ cup brown sugar, ¼ cup granulated sugar, ¼ teaspoon cinnamon and ¼ teaspoon salt. Whisk to mix.
Add the cold butter cubes to the bowl and use your fingers to work the butter into the flour mixture until it just starts to clump together and all of the butter pieces are worked into the flour and sugar mixture.
By this time, the apples should have released some of their juices. Stir the apple mixture to make sure everything is well combined and then pour the apples and their juices into the chilled pie crust. Arrange the apples into an even layer in the pie crust as best as possible.
Evenly sprinkle the topping over the apples.
Preheat oven to 400° F with a rack in the lower third of the oven. Refrigerate the pie while the oven preheats.
Bake the pie at 400° for 20 minutes, then reduce oven temperature to 350° F. Continue baking the pie for 45-50 minutes more, until the filling is bubbly. Check on the pie partway through the baking time and loosely cover it with foil as needed to prevent the crust and topping from over-browning. (I usually cover with foil about 10-15 minutes after reducing the oven temperature.)
Let the pie cool at room temperature for at least 2 hours before serving to allow the filling to thicken.
Store pie at room temperature for up to one day, or in the refrigerator, covered with plastic wrap, for up to 3 days.