Preheat oven to 350 degrees.
Measure the dry ingredients and mix together.
Whisk the remaining 6 ingredients in bowl until thick, smooth, and emulsified.
Add the dry ingredients to the wet ingredients and mix to a smooth batter.
Scrape batter over the pre-arranged beach plums and bake for about 45 minutes. Juices should bubble along the sides, and a toothpick inserted into the middle part of the cake should come out clean.
Wearing long-sleeved potholders, remove from the oven, cover the top of the cake pan with a sheet pan, then immediately flip over and whack firmly onto the counter, hitting the top of the pan to loosen the fruit. If any fruit is stuck, put it back on top of the cake with a butter knife while hot syrup is still pliable. (Be careful—hot sugar syrup can burn!)