Fry plums, sugar and rhum on a pan so the plums get soft and a bit caramelized. Add them in you cake pan that is covered with baking paper.
Whip your eggs and sugar white and fluffy. Add in the flour, baking powder, and spices through a sieve. Pour in the oil and mix all ingredients together gently. Pour the batter on top of your plum mixture.
Bake at lower rack in 350F (175C) for 40 minutes. Cover with foil for the last 10 minutes to prevent the cake from burning. Let it cool a bit and turn upside down with the help of a plate. Decorate with powdered sugar if you wish. Eat as is with a cup of coffee or tea or serve with some vanilla sauce or a scoop of vanilla icecream.