Preheat oven to 350. Grease and flour an 8-10 inch cake pan.
In a bowl, whisk flour, baking powder, salt and cardamom (or other spice). In a mixer or large bowl, beat the butter on medium until creamy for about 3 minutes. Add the sugar and beat for another 3 minutes, add eggs (one at a time) and scrape down the bowl. Add oil, optional yogurt, vanilla and zest, beat on medium until smooth. Then, reduce the speed to low and add the dry ingredients until just incorporated. Place batter in the pan and smooth with a spatula, then arrange the plums, cut side up and press down slightly into the batter. I don’t think I added enough and would recommend overlapping the plums to enhance the moistness. Bake for 35-40 minutes, until a knife comes out clean and it is golden and puffy. Cool on wire rack. If you want to wait, you can wrap the cake for a few days.