For the cake:
3 cups all-purpose flour
1 cup granulated sugar
1/2 cup light brown sugar
2 tsp baking powder
1/2 tsp baking soda
1 tsp salt
2 tsp cinnamon
3 eggs
1 cup vegetable oil
1/2 cup sour cream
2 tsp vanilla
2 cups grated apples (2 granny smith, 2 gala)

For the apple pie filling:
3 apples, finely chopped (2 granny smith, 1 gala)
1 Tbsp unsalted butter
2 Tbsp light brown sugar
1 tsp lemon juice
1/4 tsp cinnamon

For the icing:
2 sticks unsalted butter, room temperature
3 large egg whites
3/4 cup light brown sugar
1 tsp vanilla
cinnamon to taste