Remove the butter from the fridge to allow it to soften at room temperature.
In a stand mixer, cream the butter and sugar together with vanilla extract. Next, add in one egg at a time and continue beating until the mixture is fluffy.
In a separate bowl, combine the instant oatmeal, flour, and baking powder. Add the oat mixture into the butter mixture and stir until well-combined.
Spread the dough evenly over the bottom of the cake pan.
Slice the plums in half and remove the pits. Place the plum pieces alongside the edges of the cake.
Sprinkle oatmeal, coconut flakes, and sugar over the top of the cake.
Bake at 350°F for 40 minutes or until the cake is golden brown.