Preheat the oven to 180°C (static/conventional heat).
Grease the cake pan.
Whisk the eggs with the sugar for 5 to 8 minutes with an electric whisk until the mixture becomes frothy.
Add the oil while continuing to whisk, then incorporate the yogurt and mix well.
Add the sifted flour and baking powder, then mix until a homogeneous batter is obtained.
Peel the apples: cut one into large cubes and cut the rest as needed (about 3 and a half large apples).
Pour a quarter of the batter into the mold. Toss the apple cubes in a little flour, shake off the excess, and arrange them on the batter.
Cover with half of the remaining batter, add more floured apple cubes, then finish with the rest of the batter.
Decorate the top of the cake with apple slices arranged in a rosette pattern. Sprinkle with brown sugar and dot with a few knobs of butter on top. You can mix a little cinnamon with the brown sugar before sprinkling it over the cake.
Bake for approximately 1 hour 30 minutes. Check for doneness by inserting a skewer into the center: it should come out clean.
Unmold onto a wire rack and let cool. Optionally dust with a little powdered sugar once the cake has cooled, but it's not essential.
Note: If you use a wider and shallower cake pan, check for doneness starting from 45 minutes.
Enjoy the apple cake warm or cold, optionally accompanied by vanilla custard.