This cake makes a fine change of pace dessert. The key to its success is a preliminary cooking of the apples on top of the stove. Apples in an upside-down cake should be tender and completely cooked. No crunch, please. Firm-sweet apples, such as Cameo or Braeburn, are excellent in this cake because they hold their shape and deliver a sweetness that complements the buttery brown sugar topping. Browning the butter before combining it with brown sugar and cinnamon adds a nutty caramel flavor. This cake is best when very fresh, and it reheats beautifully the next day in a warm oven for 5 to 10 minutes.