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Preheat the oven to 350 degrees F. Grease a 10-inch springform pan with some butter.
Add the apples to a large bowl and toss with the lemon zest and juice.
Whisk together the flour, baking powder and salt in a medium bowl.
In a separate bowl add the eggs, sugar and vanilla, and beat together with a whisk until well combined. Add the melted butter and whisk until smooth and incorporated. Add the flour to the wet ingredients in two additions, mixing in using a rubber spatula. The batter will be very thick. Fold in the apples.
Pour the batter into the prepared pan and place on a sheet tray. Bake until golden and a toothpick inserted into the center of the cake comes out clean (make sure you do not poke an apple!), 1 hour. Let the cake cool to room temperature and set. Run a paring knife around the sides of the cake to loosen it before removing from the pan.