In a large bowl, cream together sugar and butter with a hand mixer. Mix in each egg one at a time and beat until fluffy. Then add vanilla and yogurt. Combine dry ingredients and fold into butter mixture just until combined.
Make crumb topping. Spoon and spread half the dough evenly into the bottom of a greased, deep-dish pie pan or square baking dish. Layer apples over dough.Then layer with half the crumb topping. Repeat layers.
Bake at 350˚ for 20 minutes then cover the top with foil and bake for an additional 15-20 minutes or until a fork through the center comes out clean. Prepare icing and place in a squeeze bottle.