Preheat the oven to 160 °. Halve the plums and stone them.
Beat the eggs with the powdered sugar, a pinch of salt and the vanilla sugar for a few minutes until a fluffy mixture is formed. Stir in the oil and eggnog, then sift the flour, cornstarch and baking powder over it and whisk everything well.
Pour the dough into a 28 or 26 springform pan that has been greased or lined with baking paper and spread the plums on top with the round side down. Place an amarettini on each half of the plum.
Bake in the oven for about 45 minutes (depending on the width of the springform pan). Use the chopsticks to test whether the cake is baked through.