Line the bottom of a 9-inch springform pan with parchment paper. Butter the paper and the sides of the pan.
Peel, halve and core your apples, then chop them into medium-sized chunks. (I cut each half into four “strips” then sliced them fairly thinly — about 1/4-inch — in the other direction.)
Pile the cut apples directly in the prepared pan.
Meanwhile, in a large bowl, using an electric mixer or whisk, beat eggs with sugar until thick and ribbons form on the surface of the beaten eggs.
Beat in vanilla, then stir in flour with a spoon until just combined. The batter will be very thick.
Pour over apples in pan, using a spoon or spatula to spread the batter so that it covers all exposed apples. (Updated to clarify: Spread the batter and press it down into the apple pile. The top of the batter should end up level with the top of the apples.)
Bake in preheated oven for 55 to 60 minutes, or until a tester comes out free of batter.
Cool in pan for 10 minutes on rack, then flip out onto another rack, peel off the parchment paper, and flip it back onto a serving platter. Dust lightly with ground cinnamon and powdered sugar.