1. 1. Prepare Your Baking Pan and Oven: Preheat your oven to 350 F (175 C). Grease and flour an 8×8 inch square baking pan or line it with parchment paper, leaving an overhang on two sides for easy lifting.

2. 2. Combine Dry Ingredients for the Cake: In a medium bowl, whisk together the 1 1/2 cups all-purpose flour, baking powder, baking soda, 1/2 teaspoon cinnamon, nutmeg, and salt. Set aside.

3. 3. Cream Butter and Sugar for the Cake Batter: In a large bowl, using an electric mixer, beat the softened 1/2 cup butter and 3/4 cup granulated sugar until light and fluffy, about 2-3 minutes. Beat in the large egg and 1 teaspoon vanilla extract until well combined.

4. 4. Alternate Wet and Dry for the Cake: Gradually add the dry ingredients to the wet ingredients, alternating with the buttermilk, beginning and ending with the dry ingredients. Mix until just combined; do not overmix. Gently fold in the finely diced apple. Pour about two-thirds of the cake batter into the prepared baking pan and spread evenly.

5. 5. Prepare and Add the Cream Cheese Filling: In a separate small bowl, beat the softened cream cheese, 1/4 cup granulated sugar, egg yolk, and 1/2 teaspoon vanilla extract until smooth and creamy. Carefully spread this cream cheese mixture over the cake batter in the pan, leaving a small border around the edges. Dollop the remaining cake batter over the cream cheese layer. It doesn’t need to be perfectly spread; it will bake into a marbled effect.

6. 6. Make and Add the Crumble Topping: In another medium bowl, combine the 1/2 cup flour, 1/4 cup granulated sugar, brown sugar, and 1/2 teaspoon cinnamon for the crumble. Add the cold, cubed butter. Using your fingertips or a pastry blender, cut the butter into the dry ingredients until the mixture resembles coarse crumbs. Sprinkle this crumble topping evenly over the cake batter in the pan.

7. 7. Bake the Cake: Place the baking pan in the preheated oven and bake for 35-40 minutes, or until a wooden skewer inserted into the cake (avoiding the cream cheese layer) comes out clean, and the crumble topping is golden brown. The cake should be set and lightly golden around the edges.

8. 8. Cool Before Serving: Remove the cake from the oven and let it cool in the pan on a wire rack for at least 30 minutes before attempting to slice and serve. This allows the cream cheese filling to set properly, ensuring clean slices.