Using a hand mixer, in a large bowl, mix together cake mix, eggs, yogurt (or extra egg), corn oil, applesauce (or pudding packet), cinnamon and water. Beat until just blended.
Pour cake batter into a greased 9x12 pan. Bake at 350˚ for 18-22 minutes or until a toothpick poked through the center comes out clean.
While cake is baking, get a new bowl or clean the batter bowl, and mix together flour, sugar, brown sugar, cinnamon and cubed butter using an electric mixer. Beat on a high speed until big crumbles form. About 2-3 minutes of mixing.
Immediately spread out crumbles on a baking sheet. Put the baking sheet in the oven along with the cake, on a different rack. Bake for 4 minutes then remove from oven and scrape crumbs back into the bowl. Lightly beat the cooked crumbles using the mixer to break them up. Carefully sprinkle cooked crumbles on top of the cake so that they cook on top of the cake the last 4 minutes of baking. When done, remove coffee cake from oven and let cool.
Prepare the icing by beating powdered sugar, vanilla extract and milk together in a bowl.
To pipe the icing onto the cake, fill a plastic sandwich bag with icing and cut a small hole in the corner. Squeeze the bag of icing over the cake in a zig zag fashion.
Cut cake into 12 squares and serve warm or make ahead the night before and seal with plastic wrap once cooled until morning.