In a small bowl mix the diced apples, sugar, lemon juice, cornstarch and cinnamon and set aside.
To make the crumbs:
Mix the sugars, cinnamon, salt, and butter until smooth. Whisk in the flour until the mixture becomes a solid dough, set aside.
To make the cake:
Mix together the yogurt, vanilla and egg in a small bowl. In a large bowl sift together the flour, sugar, cinnamon, baking soda, baking powder, and salt.
Add the butter to the flour mixture and using an electric mixture, slowly whisk in the yogurt mixture.
To assemble the cakes:
Preheat the oven to 325 degrees
Spoon enough batter to cover the bottom of each pan. Top with the apple mixture, and then the remaining cake batter.
Break the crumbs into 1/2 inch thick pieces (they do not need to be even), and top the cake with the crumbs. Bake for 35-45 minutes or until a toothpick inserted into the center of each cake comes out clean – it will probably still be a little moist from the apples. Cool before serving.