Add both of the flours, buttermilk and chopped tarragon and mix until it is just combined. Spoon the batter into the prepared skillet or cake tin.
Place the plums on top of the cake batter. Bake in the oven for about 25 – 30 minutes or until a skewer comes out clean. If you have baked the cake in a tin, leave it for about 10 minutes to cool slightly before turning it out onto a cooling rack.