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Step 1
Position a rack in the middle of the oven and preheat to 350 degrees. Generously grease a 9-inch springform pan with butter or oil, line it with a parchment paper circle, and lightly butter or spray the circle.
Step 2
Peel, quarter and core the apples. Slice each quarter across into 1/4-inch thick pieces.
Step 3
In the bowl of a stand mixer fitted with a whisk attachment, or in a large bowl if using a handheld mixer, beat the eggs, sugar and salt on medium-high speed (high speed for handheld mixer) until thick and ribbony, about 5 minutes. Beat in the vanilla extract and cinnamon.
Step 4
Using a fine-mesh sieve, gradually sift a third of the flour into the egg mixture, then gently fold with a spatula until just combined and no flour streaks remain. Repeat twice with the remaining flour. The batter will be very thick.
Step 5
Place half the apples in an even, compact layer on the bottom of the pan. Cover with half the batter and use an offset spatula to spread the batter evenly over the apples. Repeat with the remaining apples and batter. Gently rap the pan a few times against the counter to get rid of air bubbles, and transfer to the oven. Bake for 50 to 55 minutes, or until a cake tester comes out free of batter and the top of sharlotka is golden brown.
Step 6
Let cool in the pan for about 10 minutes, then gently run a butter knife around the perimeter of the cake to loosen and carefully remove the sides of the pan. Using a fish spatula, gently transfer the cake to a serving platter and let cool completely.
Step 7
When ready to serve, dust sharlotka with the powdered sugar and cut into slices.