Preheat the oven to 350°F (175°C). Grease a 9x13-inch baking pan.
In a large bowl, whisk together the flour, sugar, baking powder, baking soda, salt, and cinnamon.
In another bowl, beat the softened butter until creamy. Add the eggs, vanilla extract, and sour cream, mixing until well combined.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Fold in the diced apples.
In a separate bowl, beat together the cream cheese, sugar, egg, and vanilla extract until smooth.
Spread half of the apple batter into the prepared baking pan. Pour the cream cheese filling over the batter, then dollop the remaining apple batter on top.
In a small bowl, mix together the brown sugar, oats, flour, cinnamon, and melted butter until crumbly. Sprinkle this topping evenly over the cake.
Bake for 45-50 minutes, or until a toothpick inserted into the center comes out clean. Allow to cool in the pan for at least 15 minutes before slicing.