Preheat your oven to 350ºF and lightly grease an 8×8 inch baking pan.
In a bowl, combine flour, oats, brown sugar, cinnamon, and cold butter to create the streusel topping until it resembles coarse crumbs; set aside.
In a large bowl, beat the softened butter and brown sugar until fluffy.
Add the egg, sour cream, and 1 teaspoon of vanilla extract, mixing until smooth.
Fold in the flour, cinnamon, and baking powder until just combined, then stir in the diced apples.
In a separate small bowl, whip the cream cheese with the remaining teaspoon of vanilla extract until creamy.
Spread half the batter into your prepared pan.
Drop spoonfuls of the cream cheese mixture over the batter and gently swirl with a knife.
Top with the remaining batter, then sprinkle the reserved streusel over the top.
Bake for 40 minutes or until a toothpick comes out clean.