For the filling: Combine the cranberries, ½ cup granulated sugar and the water in a small saucepan over medium heat. Bring to a simmer and cook until the cranberries burst and thicken, about 10 minutes; set aside to cool.
For the topping: Combine the flour, brown sugar, oats and cinnamon in a medium bowl. With a pastry cutter or your hands, work in the butter until large clumps form. Place in the refrigerator to chill.
Continue to make the filling: Toss together the apples, remaining ¾ cup granulated sugar, the lemon juice, cinnamon, ginger, cardamom, salt and flour in a large bowl. Add the cranberry mixture and stir to combine.
For the crust: Preheat the oven to 400˚. On a lightly floured surface, roll out the dough round so it’s slightly larger, about 12 inches in diameter. Ease the dough into a 9-inch pie plate. Fold the overhanging dough under itself and crimp as desired. Pour in the apple mixture and sprinkle with the crumb topping. Refrigerate until firm, about 20 minutes.
Bake the pie for 20 minutes, then reduce the oven temperature to 375˚ and continue baking until golden brown and bubbling, about 50 more minutes. Transfer to a rack to cool completely.