Preheat the oven to 350°F and grease an 8x8-inch baking dish.
Toss apples with 2 tablespoons sugar and 1/2 teaspoon cinnamon. Set aside.
Beat softened cream cheese with 1/4 cup sugar, 1 egg, and vanilla extract until smooth.
In a large bowl, whisk melted butter and 1/2 cup sugar. Add sour cream, egg, and vanilla, mixing well.
Stir in 1 cup flour, baking soda, baking powder, and salt until just combined.
Spread half the batter into the prepared pan. Layer with cream cheese filling, then apple mixture. Top with remaining batter.
Make the streusel: combine 1/3 cup flour, brown sugar, and cinnamon, then cut in butter until crumbly. Sprinkle over the cake.
Bake for 40–45 minutes, or until a toothpick comes out clean. Cool before slicing.