Preheat the oven to 350 degrees F (175 degrees C). Grease and flour a 9x13-inch pan.

To make the topping: Mix walnuts, both sugars, and cinnamon together in a bowl.

To make the cake: Mix flour, both sugars, cinnamon, baking soda, and salt together in a large bowl. Make a well in the center and pour in sour milk, oil, and eggs. Beat with an electric mixer until smooth, then fold in chopped apples.

Pour batter into the prepared pan and sprinkle topping mixture evenly over top.

Bake in the preheated oven until a toothpick inserted into the center of the cake comes out clean, about 45 minutes.