Place the diced Granny Smith apples, granulated sugar, cinnamon, cornstarch, and water in a medium saucepan. Stir until the apples are evenly coated.
Cook over medium heat for approximately 5–6 minutes, stirring as necessary, until the fruit begins to soften and the surrounding liquid develops a thick consistency.
Take the saucepan off the heat and leave the apple filling to cool while the remaining components are prepared.
Stir the packed dark brown sugar and ground cinnamon together in a small bowl until evenly blended. Reserve this mixture for layering the cake.
Heat the oven to 350°F (175°C). Lightly coat a 9 × 13-inch baking pan with nonstick cooking spray.
Using a stand mixer fitted with the paddle attachment, cream the softened unsalted butter with the granulated sugar for about 3 minutes, or until the mixture becomes pale and fluffy.
Add the unsweetened applesauce, vanilla extract, and eggs. Beat at medium speed until thoroughly incorporated, stopping to scrape down the sides of the bowl when necessary.
In a separate mixing bowl, whisk together the all-purpose flour, baking powder, baking soda, kosher salt, and ground cinnamon.
Add the flour mixture and Greek yogurt to the butter mixture in alternating portions, starting and finishing with the dry ingredients. Sour cream may be used in place of the Greek yogurt as indicated in the original preparation.
Mix only until the batter comes together. Avoid excessive mixing, which can produce a less tender texture. Finish folding the batter gently with a spatula if necessary.
Transfer half of the prepared batter to the greased baking pan and spread it into an even layer.
Distribute the cooled apple filling over the batter, gently spreading the apples across the entire surface.
Scatter approximately two-thirds of the cinnamon-brown sugar mixture evenly over the apple layer.
Carefully spread the remaining cake batter over the apples. Finish by sprinkling the reserved one-third of the brown sugar mixture across the top.
Place the assembled cake in the preheated oven and bake for 35–40 minutes. The cake is ready when the center is set and a toothpick inserted into the middle comes out clean.
Keep the baked cake in its pan for glazing. If the surface begins to darken too quickly, loosely cover the cake with aluminum foil during approximately the final 10 minutes of baking.
While the cake completes its baking time, whisk the sifted powdered sugar, whole milk, and vanilla extract together in a medium bowl until completely smooth.
Once the cake is baked and still warm, use a butter knife to make approximately 30 holes across the surface.
Immediately pour the prepared vanilla glaze over the warm cake and spread it evenly with a spatula.
Allow the glaze to set for approximately 20 minutes before slicing and serving.