Mix 3 cups all-purpose flour with 2 teaspoons baking powder and pour the mixture into a large bowl. Add 1 cup granulated sugar, 1 egg, and 1 Tablespoon lemon zest. Cut 14 Tablespoon unsalted butter into smaller slices and add it to the bowl.
Work everything into irregular clumps with your fingers. If you prefer an electric mixer, use short pulses only, just until clumps form.
Peel and core 3 pounds apples, then shred them on the large holes of a box grater. Keep all the juice in the bowl.
Stir ⅔ cups granulated sugar, 2 Tablespoons cornstarch, ½ teaspoon groung cinnamon, and ½ teaspoon vanilla paste into the shredded apples until combined.
Line a 9x13-inch baking pan with parchment paper. Preheat the oven to 340 °F.
Divide the crumb mixture into two equal halves. Spread one half over the bottom of the pan. Add the apple layer and smooth the surface, then sprinkle the remaining crumbs evenly on top.
Bake for 40 minutes, or until the surface turns golden brown.
Notes
Oven: Temperatures are for a conventional (non-fan) oven. For convection, lower the temperature by 25°F.
Butter: One stick of butter weighs 4 oz (113 g) and equals 8 Tablespoons or ½ cup. US butter wrappers have Tablespoon markings printed on them, so you can slice off exactly what you need.
No kitchen scale? One large apple weighs about 8 oz (220 g). Use that to estimate the amount you need.
Parchment paper: To keep the paper from curling or sliding, crumple it into a ball, dip it in water, squeeze out the excess, and spread it flat in the pan.
Juice: Do not drain the shredded apples. The cornstarch thickens their juice and keeps the cake moist.
Store: Covered on the counter for 2 days, in the fridge up to 5 days, or frozen for at least 3 months.