Preheat oven to 350ºF and grease an 8x8 inch pan.

Streusel topping: Combine all the streusel topping ingredients in a small bowl. Mix with a fork, or your fingers, until the mixture resembles crumbs. Set aside.

Mix wet ingredients: In a large bowl beat together 1/4 cup butter and 3/4 cup brown sugar with an electric mixer until light and fluffy. Add egg, sour cream, and vanilla and mix to combine.

Mix dry ingredients: Stir flour, cinnamon, baking soda, and salt together in a bowl. Add to the butter mixture and stir to combine.

Add apples to the batter. Pour batter into prepared baking dish and smooth into an even layer.

Cream cheese filling: Use electric mixers to mix together the cream cheese, sugar, and vanilla until smooth. Spread over the cake batter in the pan.

Top with streusel topping.

Bake for 35 to 40 minutes. Cool in the pan for at least 10 minutes before serving.