Preheat the oven to 350 degrees F. Generously butter a 9-inch glass pie dish and arrange the plums in the dish, cut side down.
Pour 3/4 cup the coconut nectar or agave nectar evenly over the plums.
Meanwhile, cream the 6 tablespoons of butter and the remaining 1/2 cup of coconut nectar or agave nectar in the bowl of an electric mixer fitted with the paddle attachment, until light and fluffy. Lower the speed and add the flax "eggs". Add the Greek-like yogurt, zest, and vanilla and mix until combined. Sift together the flours, baking powder, and salt and, with the mixer on low speed, add it to the butter mixture. Mix only until combined.
Pour the cake batter evenly over the plums and bake for 30 to 40 minutes, until a cake tester comes out clean. Cool for 15 minutes, then invert the cake onto a flat plate. If a plum sticks, ease it out and replace it in the design on top of the cake. Serve warm or at room temperature.