Mix flour, brown sugar, 1/2 cup of white sugar, 1/2 teaspoon cinnamon, nutmeg, and salt together in a bowl. Combine butter with the flour mixture using fingers or a fork until coarse crumbs form. Stir in walnuts and set aside.
Whisk together 1/3 cup sugar, cornstarch, ginger, and 1/2 teaspoon cinnamon. Place the apples in a slow cooker, stir in the cornstarch mixture; toss with lemon juice. Sprinkle the walnut crumb topping on top. Cover and cook on fast/stew for 30 - 40 minutes, or until apples are tender.