Make the plum caramel.  In a high powered blender, place the plums, pitted and quartered.  Add the lemon juice and blend until smooth.  If the mixture is too thick to blend, add a bit more lemon juice or water.  Set aside.  Puree may be made 1 day ahead, covered, and refrigerated.

In a medium saucepan, place the vanilla bean, scrapings and whole bean, sugar, and water.  Cook over medium high heat until the sugar dissolves and the mixture bubbles vigorously, about 5 minutes.  Add the plum puree slowly and whisk to combine.  Cook about 5 minutes more until thickened.  Pour into a bowl to cool.  Once cool, refrigerate, covered, for up to 1 week.

Preheat oven to 350 degrees F.  Oil a 9 inch cake or pie pan, and place it on a foil lined baking sheet to catch any drips.

Whisk together the flour, baking powder and soda, cardamom, cinnamon, and coconut and maple sugars.  Whisk in the olive oil and egg yolks, followed by the milk.  Whisk until a relatively lump free batter forms.

Pour half the batter into the prepared pan.  Top with 1/3 cup of caramel.  Pit the plums and cut them into wedges about ¾ inch thick.  Top the caramel with half of the plum wedges.

Pour the remaining batter on top, spread over the plums, then add the rest of the plums (squeeze them in!), sprinkle with the reserved tablespoon of sugar, and bake for an hour to 1 hour 20 minutes, tenting if necessary to prevent browning.  The cake is done when it is golden brown and a toothpick inserted in the center comes out clean.

Serve warm or allow to cool completely in the pan.  Cake may be stored in an airtight container at room temperature for up to 5 days.  Be sure to serve it with extra caramel!