Preheat the oven to 180°C (350°F).
Remove the pineapple slices from the jar and drain them in a colander, then place them on paper towels to dry thoroughly.
Arrange the slices flat on the caramel, side by side in a circle, with one in the center. Place a candied cherry in each hole and set aside.
Melt the butter and let it cool slightly.
In a bowl, whisk the eggs with the sugar and vanilla sugar until the mixture becomes frothy. There is no need to bleach them or triple their volume.
Add the lukewarm melted butter while continuing to mix, then add the pineapple syrup.
Incorporate the sifted baking powder, mixing well, then add the flour and mix until smooth.
Optionally, fold a few pineapple rings cut into pieces into the batter.
Pour the batter into the pan and bake for approximately 45 to 55 minutes. Check for doneness after 45 minutes by inserting a wooden skewer into the cake. It should come out clean.
Tip: You can butter the sides of the round cake pan to make unmolding easier. I don't butter the sides of my cake pan, and the cake comes out perfectly. You can get a thicker cake by using a smaller pan. I find that this gives nice slices that are neither too thin nor too thick.
Optionally, soak the cake with a few spoonfuls of syrup when it comes out of the oven, then return it to the turned-off oven for five minutes.
Unmold the cake onto a serving dish and let it cool or just warm slightly before enjoying.