Make the streusel: In a medium bowl, mix together the flour, sugar, brown sugar, and cinnamon. Pour in the melted and cooled butter and combine to form a sandy mixture. Set aside.
Preheat oven to 350℉. Spray a 9x13 pan with baking spray.
Make the cake: First, peel, core and dice the apples. Then, in the bowl of a stand mixer, add the flour, sugar, baking powder, baking soda, and salt. Using the paddle attachment, mix for about 30 seconds.
In a medium bowl, whisk together the eggs, 1 cup of sour cream and the vanilla extract until combined.
Add the butter and ½ cup sour cream to the flour mixture in the stand mixer. Mix until crumbly, about 45 seconds.
Add one third of the egg mixture to the stand mixer and mix for 30 seconds. Scrape the sides and bottom of the bowl. Add another third, mix for 30 seconds, scrape again and then add the last of the egg mixture. Mix for 30 seconds on low speed.
Turn mixer up to medium and mix for about 45 seconds until the mixture is smooth.
Pour about half of the batter into the prepared pan. Sprinkle the diced apples on top of the batter. Sprinkle about 1 cup of the topping mixture over the apples.
Pour the remaining batter over the apple/streusel layer and spread carefully to keep the layers seperate.
Sprinkle on the remaining streusel mixture to cover the top of the cake.
Bake for 45 minutes or until the a toothpick inserted in the center of the cake comes out clean. Allow to cool at room temperature for at least an hour before serving so that the cake slices well.