Make the Filling: Cook apples, sugar, cinnamon, cornstarch, and water in a saucepan for 5-6 minutes until soft and thickened. Cool.
Prepare Brown Sugar Mix: Combine dark brown sugar and cinnamon in a small bowl and set aside.
Preheat Oven: Heat oven to 350°F and coat a 9×13 pan with nonstick spray.
Mix Wet Ingredients: Beat butter and sugar until fluffy, then mix in applesauce, vanilla, and eggs.
Combine Dry Ingredients: Whisk flour, baking powder, baking soda, salt, and cinnamon in a bowl.
Make Batter: Alternate adding the dry mixture and Greek yogurt to the wet ingredients, starting and ending with the dry.
Assemble: Spread half the batter in the pan, top with apple filling, 2/3 of the brown sugar, and remaining batter. Sprinkle the rest of the brown sugar on top.
Bake: Bake for 35-40 minutes until the center is set.
Add Glaze: Mix powdered sugar, milk, and vanilla for the glaze. Poke holes in the hot cake, pour glaze over, and let set for 20 minutes before serving.