Peel and core apples; slice into thin wedges. In a large bowl, stir together apples and cranberries. Turn into an 11x9-inch baking dish.
In a bowl, stir together flour, rolled oats, sugar, ginger, cardamom, and cinnamon.
Using fingers, work in butter until pea-size crumbs form. Sprinkle over fruit.
Bake in 350F oven until bubbling around edges and topping is set and deep golden brown, about 1 hour. Check after 45 minutes; if topping is becoming too dark, cover loosely with foil. Let stand about 10 minutes before serving.