Grease a 9x13 inch baking dish and dust with flour (or line with parchment paper). Set aside. Preheat your oven to 350°F.
In a large bowl, combine flour, baking powder, salt, and sugar. Whisk to combine. Divide the dry ingredients in half and set aside one half for later (about 1 and ¾ cups for each portion).
Make the cake layer: In a large bowl, combine half of your dry ingredients (about 1 and ¾ cups) and the butter. Cut the butter into the dry ingredients until your get a mixture that resembles fine breadcrumbs.
Add the eggs, milk, and vanilla extract to the bowl. Whisk together until the batter just comes together. Take care not to over mix! Some lumps are fine. Pour the cake batter into the prepared baking dish. Spread into an even layer, and set aside.
Make the apple layer: In a medium bowl, combine apples, brown sugar, and cinnamon. Stir together until the apples are fully coated in the sugar and cinnamon. Evenly sprinkle the apples over the cake layer. Set aside.
Make the crumb topping: In a large bowl, combine the remaining half (1 and ¾ cups) of the dry ingredients and an additional ½ cup of flour. Whisk to combine.
Add in the other stick of butter. Again, cut the butter into the dry ingredients until the mixture resembles fine crumbs. Add 4 tablespoons of water and mix. You should be left with a crumbly mixture that sticks together when pinched. If it's too dry, work in more water, 1 tablespoon at a time, until it reaches the right texture.
Sprinkle the crumb topping evenly over the apple layer. Bake the cake in the center of a preheated 350°F oven for 30 to 35 minutes, or until golden brown on top and a skewer inserted into the center comes out clean. Cool slightly before slicing.