Mix flour with baking powder and pour it into a large mixing bowl. Add granulated sugar, egg, and grated lemon zest to the dry ingredients. Add the butter cut into smaller slices.
Use your fingers to work everything into irregular clumps. Expect this step to take some time and maybe even physical effort, but it's nothing you can't handle!
Prepare the apples: Skin the apples with a peeler. Then cut out the apple core. I use a simple tool for this: a core remover. Place the peeled apples in a medium bowl. Using a hand grater box, shred the apples on the side with large holes. Don't drain the juice from grated apples!
Add the sugar, ground cinnamon, vanilla, and cornstarch to the shredded apples. Stir until combined.
Line a baking dish with parchment paper. I have a simple trick for keeping the paper from curling or sliding on the pan's surface: Crumple the baking paper into a ball, dip it in water, squeeze it, and spread the paper out again. Then place it on the bottom of the baking pan.
Make the apple cake with three layers. Divide the crumbs into two equal halves. Spread one half of the crumbs on the bottom of a lined baking pan. Continue spreading the apple layer, smoothing the surface well. Sprinkle the apples evenly with the other half of the crumb mixture.
Preheat the oven to 340°F/170°C (lower and upper heat). Place the pan with the apple cake in the oven and bake for 40 minutes until the surface turns golden brown.