In a medium saucepan, combine diced Granny Smith apples, white sugar, cornstarch, and ground cinnamon over medium heat. Stir frequently and cook for about 5-7 minutes, until the apples soften and become fragrant. Remove from heat and let cool.

Preheat your oven to 350°F (175°C) and generously grease a 9x13-inch baking pan with unsalted butter.

In a large mixing bowl, cream together room-temperature butter and white sugar until light and fluffy, about 2-3 minutes. Add applesauce, vanilla extract, and large eggs; mix until smooth.

In a separate bowl, whisk together all-purpose flour, baking powder, baking soda, kosher salt, and a pinch of ground cinnamon. Gradually fold this into the wet batter, alternating with Greek yogurt. Mix just until combined.

Pour half of the batter into the prepared pan, spreading it evenly. Spoon the cooled apple mixture over the batter, ensuring it is distributed evenly. Sprinkle half of the cinnamon sugar mixture over the apples, then add the rest of the batter. Finish with more cinnamon sugar on top.

Bake the cake for 35-40 minutes until a toothpick inserted in the center comes out clean. Allow it to cool in the pan on a wire rack.

While the cake cools, whisk together powdered sugar, milk, and vanilla extract. Adjust milk as necessary for desired glaze consistency.

Poke holes across the top of the cake with a toothpick, pour the glaze over, and spread if necessary. Allow the cake to cool completely before slicing and serving.