Put apples and cranberries in a large pan with the white sugar. Stir to combine, then cover and place over medium-low heat for about 15 minutes, stirring two or three times. The apples should be soft not mushy.
Transfer the fruit to a 13 x 9 inch baking dish and let cool while you prepare the topping.
Topping:
Preheat the oven to 350 degrees F.
In a bowl, blend the brown sugar and butter, then add the flour and oatmeal and mix until it resembles very coarse crumbs.
Stir in the chopped walnuts.
Sprinkle the crumbly mixture over the fruit. Bake 30 – 35 minutes or until golden brown on top and the juices are bubbling.