adapted from Smitten Kitchen
Note: This is the way I wish I'd made it. The original recipe had you pile the apples in the pan, then spread the very thick batter over the top and hope it sank in. This resulted in a layer of apples topped by a layer of cake.
2/3 c sugar
1 tsp vanilla
2/3 c flour
4 apples, chopped
Beat eggs and sugar until thick. (If you beat too long, you'll have a meringue-like shell on the top of the cake.) Beat in vanilla, then stir in flour with a spoon. Stir in apples.
Scrape batter into pan. Bake 55 to 60 minutes.