Preheat the oven to 350 degrees F (175 degrees C). Liberally coat a 7x11-inch baking dish with cooking spray.
Without peeling, slice plums and discard pits. Place plums in a bowl and toss with 1 teaspoon vanilla sugar, depending on their sweetness. Set aside.
Sift 2/3 cup vanilla sugar, flour, butter granules, baking powder, cinnamon, and salt together in a large bowl. Stir until well blended.
Whisk orange juice and liquid egg together in a 2-cup liquid measure until well mixed. Blend in oil. Pour into the dry ingredients and stir until thoroughly blended but not overmixed. Pour into the prepared baking dish and cover with sugared plums.
Bake in the preheated oven until cake is golden and plums are soft and juicy, 55 to 60 minutes.
Remove from the oven and allow to cool for 30 minutes. Slice into 12 pieces and serve.
A pan smaller than a 7x11 inches produces a cakier pastry.