Roll out pie crust and fit to a 9-inch pie pan. Trim and crimp as desired, then transfer to the freezer to chill while you prepare the filling.
Put chopped apples into a bowl filled with cold water and a dash of lemon juice to prevent browning. Add cranberries to a food processor and pulse a couple of times to roughly chop.
Add butter to a large pan and heat over medium. Once the butter is melted, stir in sugars, melting slightly. Stir in drained apples and chopped cranberries. Add flour, cinnamon, ginger, and nutmeg, and stir well to coat fruit. Cook for about 10 minutes, until liquid is syrupy. Remove from heat and let cool briefly while you prepare the topping.
To make the topping, combine flour and brown sugar in a small bowl. Cut in butter with a pastry blender, knife, or your fingers, until evenly mixed and clumps form.
Remove pie crust from the freezer and place on a rimmed baking sheet (to catch spilled juices). Pour in the filling, then scatter the crumble topping on top of the pie.
Bake the pie at 425°F for 10 minutes, then reduce the oven to 350°F and continue to bake for 40-50 minutes, until browned and bubbly.
Remove from the oven and let cool completely before slicing and serving.
Notes
If using a pie shield, add it before placing the pie in the oven.
If the topping is browning too quickly, drape a piece of foil over the top of the pie.