Preheat the oven to 350 F (180 C)
Grease 8 small bread molds and set aside.
In a bowl, combine the flour, baking powder, salt, and cardamom.

In the mixer bowl, cream the butter and sugar until the mixture is smooth.
Add the eggs one by one, mixing well between each addition.

Add the oil, orange zest, and vanilla, and mix well.
Add the dry ingredients, mixing gently.

Divide the mixture among the small bread molds and place the plum halves on top, pressing gently to sink them slightly.

Bake for 35 minutes or until a knife inserted in the middle comes out clean.
Let cool on a wire rack for 15 minutes before serving.