Bring the egg and butter to room temperature. Sift together the flour and baking powder. Set aside.
Leaving the peels intact, cut the apples into fourths, remove the seeds, and cut each fourth into 6 thin slices (24 slices in total).
Put the sugar in a frying pan and cook while stirring on a medium-low until it becomes a rich brown.
Add the apples, shake the pan and flip the apples to coat them completely. When the apples turn brown on both sides, turn off the heat and let cool.
Using a spatula or chopsticks to mix the caramel is a little difficult, so I just shake and flip.
Line your pan with parchment paper.
Preheat the oven to 180°C and set the timer to 40 minutes.
Whip the butter with a whisk until it turns white. Add the sugar in 4-5 portions and knead into the butter until fluffy.
Beat the egg well, then mix it into the sugar and butter in 5~6 parts. Don't add it all in.
Add the sifted dry ingredients all at once and mix well until fluffy and no longer powdery.
Add a couple drops of vanilla and knead well.
Arrange the caramelized apples into the pan from Step 6 into a single layer. Don't add any remaining juice or caramel.
Pour the batter into the pan and smooth the top. Drop from a few centimeters up 2~3 times to remove any air bubbles from the batter.
Bake for about 35 minutes. If the surface is nicely browned and a toothpick or skewer inserted in the center comes out clean, it's ready.
When it has cooled, flip the cake out of the pan and onto a plate. Wrap with plastic and let cool.
It's good while still warm, but it tastes even better if you let it sit in the refrigerator overnight.
Story Behind this Recipe
I made this because I got a lot of apples.
When making the batter, be sure to add the sugar and the egg in parts, not all at once. Also, if the egg is still cold, Step 9 will become difficult, so be sure to bring it to room temperature. The ratio of sugar to apples for the caramelized apples is 10 g of sugar per 50 g of apples.