Prepare the pie crust up to step 5 and chill it.
Make the crumble topping by mixing brown sugar, flour, cinnamon, and butter until crumbly. Stir in oats, then refrigerate.
Preheat the oven to 400°F (204°C) and place a baking sheet on the bottom rack.
Roll out the chilled dough into a 12-inch circle and place it in a 9-inch pie dish, crimping the edges. Brush with egg wash and refrigerate for 10 minutes.
In a bowl, mix apple slices, cranberries, brown sugar, flour, orange zest, cinnamon, allspice, and nutmeg.
Spoon the filling into the chilled crust and sprinkle the crumble topping on top.
Bake for 20 minutes, then reduce the temperature to 375°F (190°C) and continue baking for 35-40 minutes, covering edges with a pie crust shield.
Cool for at least 3 hours before slicing. Store leftovers at room temperature for 1 day or in the fridge for up to 5 days.