First, make the caramel sauce. Put the caramel sauce ingredients in a pot, heat on medium, melt the sugar and slowly simmer until golden brown. Turn off the heat, then place pot on a damp towel, allow to cool to harden the caramel.
While waiting for the caramel to harden, prepare the apples and preheat the oven. Peel the apples, cut in half, core, then thinly slice into 2 to 3 mm wedges. Preheat the oven to 250°C.
After the caramel hardens, coat the caramel surface and the sides of the pot in butter. Since the butter and caramel will melt when baking, don't be concerned if they are lumpy. I recommend using your fingers to spread the butter after measuring it out.
Line the surface of the caramel with the sliced apples. After placing 2 or 3 end slices, lay the rest of the slices around in a circle while overlapping them. (Arranging the slices nicely will give the cake a pretty finish, but for those who don't mind, just lay the pieces flat.)
Put the pot in the oven preheated to 250°C and bake for 12 minutes. If you have space on top of the oven (outside the oven), put the butter for the batter in a heat-resistant dish and simply let the butter melt in residual heat from the oven.
While baking the apples, let's make the batter! Put the almond powder, sugar, and egg white in a bowl, thoroughly mix together with a rubber spatula, then add the egg yolk, apricot jam, and lemon juice, then thoroughly mix to incorporate air.
The apples should be done. Remove the pot from the oven, gently tip the pot, then pour out the juice from the baked apples into a separate dish to adjust the water content. Keep the leftover juices as it'll be used later.
After adjusting the water content, re-position the apple slices in the pot. If there are any gaps or if the apples are not lying flat, use a spoon to press flat.
Set the oven to 200°C. For the batter, sprinkle the butter into the batter from Step 6, mix until smooth, then pour in the leftover apple juices and stir.
Combine the cake flour and baking powder and sift into the bowl, then, with a rubber spatula, fold in with cutting motions without kneading. Thoroughly mix until the batter becomes shiny. (With the rubber spatula, repeatedly trace a "J" on the bottom of the pan while turning the bowl towards you.)
Pour the batter into the pot, then level it out. Bake for 8 minutes in an oven preheated to 200°C, reset oven to 180°C, then bake for 12 minutes, then reset oven to 170°C and bake for 3 more minutes.
It should look like this fresh from the oven. Pierce it with a skewer, and if it comes out clean, it's finished! Place a sheet of aluminum foil over the pot, and let's wait for the cake to cool. (If overbaked, the cake will be crumbly and dry).
When the cake cools, with the aluminum foil in place, firmly hold the pot, and lightly agitate (give it a good, hard shake to dislodge the contents.) The caramelized apples should separate from the pot, and the cake should come out easily.
If the cake doesn't want to come out, or if the caramel has hardened and the cake won't budge, heat the pot over the stove and it should come right out. If you force it, the apples will end up a tragic mess, so be careful when removing the cake!
Remove the aluminum foil, hold the pot over a dish one size larger than the pot, then carefully flip the pot over.
It should look like this.
Slice into desired size pieces and serve.
Story Behind this Recipe
I based this recipe on Makiko Fujino's "Tart Tartin Style Cake" and adjusted the ingredients to my preference and also reduced the amount of tools used to save on clean-up time.
I use a Teflon-coated deep pot with removable handles that can be used in the oven. This saves on clean-up time and is simple and easy for cooking! But it's fine to use a pot with handles that can be put in the oven. If you don't have one, make the caramel in a small sauce pan, then pour it into a round cake pan. The cake is delicious fresh from the oven, but if you let it sit for 1 to 2 days, the caramelized apples will blend into the cake and it will become nice and moist.