Preheat the oven to 180 degrees Celsius/ 350 degrees Fahrenheit. Butter a cake dish of about 26 cm/10-inch diameter, not a springform, or the running juices of the plums, will make a mess in your oven.
Prepare plums: Halve the plums and arrange them nicely in the dish with the cut side up. Try to cover as much space as possible, even if the plums overlap here and there.
Mix the flour, salt, baking powder, and spices in a bowl.
Heat the milk very gently in a small pan (and whisk in the turmeric paste, if using that instead of the spices).
Melt the butter in a small pan.
Batter: In another bowl, whisk the eggs, sugar, and vanilla extract until pale and fluffy. Add the milk and incorporate. Sieve the flour mixture over the egg mixture and fold in carefully. Fold in the melted and slightly cooled butter as well.
Bake: Pour the batter over the plums and bake for about 30-35 minutes or until the cake is set in the middle.
Let rest in the pan for about 20 minutes, then invert onto a cake platter. Let cool completely.
Serve the cake as it is or with whipped cream.