Preheat oven to 350F. Grease an 8x12 inch cake pan with butter.
Beat the eggs and sugar together in a bowl with a handheld mixer for at least 5 minutes (use a timer if necessary) until very thick, pale, and foamy. The amount of air you beat in is essential.
Gently fold the flour and a good pinch of salt into the egg mixture.
Mix the cinnamon with the apples, then tip the apples into the prepared cake pan and pour the cake batter evenly over the apples. Bake until a skewer inserted into the cake comes out clean, 35 minutes.
Let it cool in the pan. Dust with some icing sugar, cut into squares and serve.