Liberally grease a 9 or 10 inch cast iron skillet, or other pan of similar size, with half of the butter. Yes, you heard me right, half of the butter. It would be sad if your cake stuck to the pan.
Sprinkle the bottom of the skillet with the brown sugar and lemon zest, then add the plums in a single layer, cut side down.
Whisk together the remaining butter, yogurt, eggs, sugar, and lemon juice.
In a separate bowl, combine the flour, baking soda, salt, and cinnamon.
Add the liquid mixture to the flour mixture, and stir gently to combine.
Pour the batter into the skillet, on top of the plums, smoothing and leveling the top.
Bake for 50-60 minutes, or until a toothpick stuck in the center comes out clean.
Let cool for only about 5 minutes. Now it’s time to flip… don’t be scared!
Put a plate that is larger than the skillet over the top. Using hot pads (I highly recommend the hot handle holder you see in the picture above), carefully flip the cake over and gently lift the pan off the cake. This is the moment of truth. But really, all that butter should have helped!
It’s common for some of the fruit to stick to the pan. As long as your cake is intact (I’m sure it will be), you can do a bit of fruit repair and no one will ever know. And just like that you have a gorgeous upside-down cake!