• Take the eggs and Greek yogurt out from the fridge to let them come to a room temperature while you are preparing other things
• If you forget to take the eggs out early, place the eggs in a bowl of warm (not hot) water for about 10-15 minutes. This method gently warms the eggs without cooking them.
• Do the same with the yogurt. Scoop out the amount you need into a bowl and warm the bowl over another bowl of hot water
• Preheat the oven to 350 F (180 C) conventional oven, 330 F (165 C) for convection oven

Prepare the plum topping:

• Use a 9 x 2 round cake pan. Make sure it is at least 2 inches in height. Grease just the side of the pan so you can easily release the cake later
• Rub the softened butter all over the bottom of the pan.
  
• Sprinkle evenly with sugar. This mixture will caramelize as the cake bakes
  
• You want to use plums that are ripe but still firm. Insert a knife into the plums, touching the stone the whole time and move the knife all around. Twist the plum in an opposite direction. Remove the stone with the knife. Slice the plums into 1/4 inch slices
• Arrange the plum slices decoratively, slightly overlapping if you like, starting from the edge and working your way toward the center
  
• 

Prepare the cake batter:

• Whisk oil and sugar vigorously for about 30-40 seconds.
  
• Add room-temperature eggs and whisk again and you will see the mixture emulsifies.
  
• Add the Greek yogurt, baking powder, baking soda, and salt and whisk again to combine
  
• Sift in all-purpose flour and matcha powder. Use a spatula to fold the dry mixture into the wet. Do not overmix. As long as you don't see any pockets of flour, you are done mixing. It is a lumpy batter and that's ok
  
• Scrape the cake batter into the pan, covering the plum slices. Use a spatula to smooth the top
  

Bake the cake:

• Bake the cake on the middle rack for 40-45 minutes or until a cake tester inserted into the center comes out clean with a bit of moist crumbs is okay. The surface of the cake shouldn't be wet anymore and when you gently press on it, it bounces back
  

Invert the cake:

• Remove from the oven and let it sit for 5 minutes
  
• Take a large round serving platter and place on top of the pan and quickly and carefully invert the cake onto the platter. Then gently remove the pan. Some plums may get stuck to the pan. Just remove it and put them back on top of the cake. Any extra caramel on the pan, you can pour it on the surface of the cake
  

Cool down:

• Let the cake cool down for at least 30 minutes or to a room temperature before slicing it. They are the best served on the same day but they also stay moist when you keep them at room temperature in an air-tight container for 2-3 days