Preheat the oven to 350 degrees Fahrenheit. Grease an 8-inch cake pan and line the bottom with parchment paper.
For the pan coating, sprinkle the 1/3 cup sugar over the bottom of the pan. Cut the butter into small pea-sized bits and evenly distribute across the bottom of the pan.
Cut the plums in half and remove and discard the pits. Place them in a single layer, cut-side-down, on the bottom cake pan.
In a large bowl, mix together the flour, cinnamon, baking powder, allspice, cloves, nutmeg, and salt until combined. Set aside.
In the bowl of an electric mixer fitted with the paddle attachment, mix together the granulated sugar and the olive oil. Add the eggs, one at a time, beating well after each addition. Add the vanilla and almond extracts and mix until thoroughly combined.
Add the flour in two increments, mixing until *just* combined. You should now have a smooth, and fairly thick, cake batter.
Pour the cake batter over the plums in the cake pan. Place the pan in the oven and bake for about 1 hour 10 minutes, or until a toothpick inserted into the cake comes out relatively clean.
Allow the cake to cool for 15 minutes before flipping it over and inverting it onto a plate or cake stand and removing the pan. Peel off and discard the parchment paper. Allow the cake to cool, then transfer it to a plate and slice and serve.