Make the topping. Mix both sugars, cinnamon, and salt in medium bowl and whisk to blend. Add warm melted butter and stir to blend. Add flour and toss with fork until moist clumps form (topping mixture will look slightly wet). Set aside.
Prepare the pan. Position rack in center of oven and preheat to 350°F. Butter 13x9x2-inch glass baking dish.
Sift the dry ingredients. Sift the rest of the flour, baking soda, baking powder, cinnamon and salt into medium bowl.
Cream the butter and sugar. Using electric mixer, beat room-temperature butter in large bowl until smooth. Add sugar and beat until light and fluffy.
Add remaining wet ingredients. Add eggs 1 at a time, beating until well blended after each addition. Add greek yogurt, and vanilla extract and beat just until blended.
Add the flour gradually. Add flour mixture in 3 additions, beating just until incorporated after each addition.
Fold in chopped apples. With a rubber spatula, gently fold in chopped apples into batter.
Add crumb topping. Transfer cake batter to prepared baking dish; spread batter evenly with rubber spatula or offset spatula. Squeeze small handfuls of topping together to form small clumps. Drop topping clumps evenly over cake batter, covering completely (topping will be thick).
Bake the cake. Bake cake until tester inserted into center comes out clean and topping is deep golden brown and slightly crisp, about 1 hour. Cool cake in dish on rack at least 30 minutes. Cover and let stand at room temperature.
Make the icing. In a mixing bowl with a whisk, combine the icing ingredients until smooth. If it's too thick add a little more milk. If it's too thin, add a bit more powdered sugar. Drizzle over the cake. Cut cake into squares and serve slightly warm or at room temperature.