Pre-heat the oven to 160ºC (320ºF).
Prepare a small spring-form pan (mine is 7" / 18cm) by greasing or lining with baking paper.
Whisk the sugar and butter together until it is pale and fluffy.
Add in one egg at a time and the vanilla extract, and continue to whisk until everything is well mixed.
In a separate bowl, mix the baking powder and flour together.
Carefully fold the dry ingredients into the wet.
Pour the thick batter into the prepared tin, and give it a little shake to level if off.
Place the plums skin side down in the batter and bake for around 30 minutes. Because the cake will be put back into the oven with the topping, aim for a centre that is still a little soft.