Yield: 8 to 12 servings

Method:

To make the plums, toss them with the sugar in a large bowl. Let sit for 1 to 2 hours.

To make the cake, preheat the oven to 350ºF. Butter and flour a 9-inch loaf pan and set asisde. Sift together the flour, baking powder, and salt; set aside. Put the sugar and eggs in a stand mixer fitted with a whisk attachment. Whisk until the eggs are very light in color and the mixture has increased in volume, about 5 minutes. Whisk together the olive oil, orange juice, and vanilla extract in a small bowl. Slowly drizzle into the eggs while the stand mixer is still running. Turn off the machine and use a rubber spatula to fold in the sifted dry ingredients. Pour the batter into the prepared loaf pan and bake until golden brown and the tip of a knife comes out clean when inserted, about 30 minutes.

To make the olive oil pudding, combine the milk, vanilla bean, and half of the sugar in a small saucepan and bring to a boil. Working quickly, whisk together the remaining sugar, egg yolks, whole egg, cornstarch, and salt. When the milk has just started boiling, slowly pour it into the egg mixture, whisking constantly. Transfer the mixture to the pot and cook over medium heat, whisking constantly, until very thick, about 2 minutes.

Remove the pudding from the heat and transfer to the bowl of a stand mixer fitted with a paddle attachment. Turn the mixer on high and mix to let steam escape from the pudding. Once it has stopped steaming, drizzle in the olive oil with the machine still running. Cover the surface of the pudding with plastic wrap to keep it from forming a skin and refrigerate until chilled.

To serve, strongly stir the pudding with a spoon or spatula to loosen its texture. Slice the cake into individual servings. Serve each slice with some pudding and plum slices.