In a medium bowl, whisk together the granulated sugar, brown sugar, cinnamon, and flour.

Add the cold, cubed butter. Use a pastry cutter or your fingertips to cut the butter into the mixture until it resembles coarse crumbs with some pea-sized pieces remaining. Set aside (chill if your kitchen is warm).

Preheat your oven to 350°F (175°C). Grease and flour a 9x9 inch baking pan.

In a separate medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.

In a large bowl, use an electric mixer to beat the softened butter and granulated sugar together on medium-high speed until light and fluffy, about 2-3 minutes.

Beat in the egg and vanilla extract until well combined, scraping down the sides of the bowl as needed.

Reduce the mixer speed to low. Add half of the dry ingredients and mix until just combined. Add the sour cream and mix until just combined. Finally, add the remaining dry ingredients and mix until just combined. Do not overmix.

Gently fold in the chopped apples with a rubber spatula.

Spread the batter evenly into the prepared baking pan. It will be thick.

Sprinkle the reserved crumb topping evenly over the batter.

Bake for 40-50 minutes, or until a toothpick inserted into the center of the cake comes out clean or with moist crumbs attached. The topping should be golden brown.

Let the cake cool in the pan on a wire rack for at least 20 minutes before slicing and serving.