Preheat the oven to 180˚C fan / 200˚C / 356˚F convection / 392˚F.
Line the base of a 20 cm / 8 inch round cake tin with baking parchment.
Wash and dry the plums, remove the pit, then slice in to halves, quarters or eights, depending on their size.
In a large mixing bowl whisk the eggs with a balloon whisk or fork until fluffy.
Add the yogurt, sugar, oil, lemon zest and vanilla and beat until well combined.
Sift in the flour and baking powder and mix with a spoon until the flour is mixed in. (There will probably be some lumps in the batter, but this is ok.)
Pour the batter in to the prepared tin, then place the sliced plums on the top.
Place in the preheated oven and bake for 35-40 minutes, until a skewer inserted in the middle comes out clean. Keep an eye on the cake as the top can start to go brown in some ovens. If this happens, carefully place a piece of foil over the top and continue to cook.
Leave in the tin for 5-10 minutes, then remove from the tin and cool completely on a wire rack.
Store in an airtight container.