Preheat the oven to 350 °F (175 °C). Lightly grease a 9x9-inch (23x23 cm) baking pan with nonstick spray and line it with parchment paper, leaving enough overhang to lift the cake out of the pan. Do not use an 8x8-inch (20x20 cm) pan; there is too much batter for that size.
In a medium bowl, whisk together the flour, dark brown sugar and cinnamon. Add the cold, cubed butter and pinch it into the dry ingredients until coarse crumbs form. Press some of the mixture together and crumble it apart to create a combination of smaller crumbs and larger clumps. Refrigerate while you prepare the cake.
1 cup + 2 tablespoons (140 grams) all-purpose flour, 1/3 cup (66 grams) dark brown sugar, 1 1/2 teaspoons ground cinnamon, 1/8 teaspoon salt, 1/2 cup (113 grams) cold unsalted butter
Toss the finely chopped apple with 1 tablespoon of flour and set aside.
1 1/4 cups (185 grams) finely chopped apple, 1 tablespoon all-purpose flour
In a medium bowl, whisk together the 2 1/4 cups flour, baking powder, baking soda and salt. Set aside.
1 1/2 teaspoons baking powder, 1/2 teaspoon baking soda, 2 1/4 cups (280 grams) all-purpose flour, 1 teaspoon salt
In a large mixing bowl using a stand mixer or hand mixer, beat the softened butter and granulated sugar for 3-5 minutes, until light and airy, scraping down the sides of the bowl as needed.
1/2 cup (113 grams) unsalted butter, 3/4 cup (150 grams) white granulated sugar, scooped
Add the eggs and vanilla and beat on medium speed just until combined. Scrape down the bowl. With the mixer on low, add the applesauce and sour cream and mix just until incorporated. Do not overbeat.
2 large eggs, 2 teaspoons vanilla extract, 3/4 cup (180 grams) unsweetened applesauce, 3/4 cup (180 grams) sour cream
Add the dry ingredients and gently fold them into the wet ingredients with a rubber spatula or wooden spoon. Stop as soon as the last streaks of flour disappear. The batter should be thick and spreadable and should hold its shape when dolloped. Do not thin it with milk.
Spread about half of the batter evenly into the prepared pan. Sprinkle 1 1/2 tablespoons of the prepared streusel over the batter, followed by the chopped almonds and 3 tablespoons of dark brown sugar.
1/4 cup (40 grams) almonds, finely chopped, 3 tablespoons dark brown sugar
Gently dollop the remaining batter over the filling. Carefully spread it toward the edges of the pan, taking care not to press down hard or drag the brown sugar layer into the batter.
Scatter the flour-coated apple evenly over the batter and cover it with the remaining streusel.
Bake on the middle rack for 40-50 minutes. Begin checking at about 35 minutes. The exact baking time can vary depending on the moisture level of the applesauce and the type of pan. The cake is done when a toothpick inserted into the center comes out clean or with just a few crumbs.
Let the cake cool in the pan for 15-20 minutes. Use the parchment overhang to remove it from the pan, then serve slightly warm or transfer it to a wire rack to cool completely.