In a medium bowl, whisk together the flour, granulated sugar, brown sugar, cinnamon, and salt. Pour in the melted butter and stir with a fork or rubber spatula until the mixture is evenly moistened and begins to form large clumps.

Gently squeeze portions of the crumb mixture together with your hands to create a mixture of small and large crumbs. Set the topping aside at room temperature for 10-15 minutes while you prepare the cake batter.

Preheat the oven to 350°F. Grease a 9x13-inch light-colored metal baking pan and line it with parchment paper, leaving an overhang along the long sides for easy removal.

In a medium bowl, whisk together the flour, baking powder, baking soda, salt, and cinnamon.

In a large bowl using a hand mixer, or in the bowl of a stand mixer fitted with the paddle attachment, beat the softened butter and granulated sugar on medium-high speed for 3-4 minutes, until light and fluffy. Scrape down the sides and bottom of the bowl as needed.

Add the eggs and egg yolk one at a time, mixing well after each addition. Add the vanilla and mix until combined. The mixture may look slightly curdled after the eggs are added, which is normal.

In a separate bowl or measuring cup, stir together the applesauce and sour cream until smooth.

With the mixer on low speed, add one-third of the dry ingredients to the butter mixture. Mix just until mostly incorporated. Add half of the applesauce mixture, followed by another third of the dry ingredients. Repeat with the remaining applesauce mixture, then add the remaining dry ingredients.

Mix just until the batter is smooth and no dry streaks remain. Do not overmix. The batter will be thick and soft.

Spread the batter evenly into the prepared pan, smoothing the top with an offset spatula.

Break the crumb topping into pieces ranging from small pebbles to approximately ¾-inch clumps. Scatter the crumbs evenly over the batter, covering the surface completely. Press the crumbs very lightly into the batter so they adhere without sinking.

Bake for 45 minutes, or until the crumb topping is lightly golden and a toothpick inserted deeply into the cake layer comes out clean or with a few moist crumbs. Begin checking around 42 minutes. If the topping begins to brown too quickly, loosely tent the pan with foil. The internal temperature should be around 210°F.

Let the cake cool completely in the pan before using the parchment overhang to lift it out. Dust generously with powdered sugar immediately before slicing and serving.