Preheat oven to 350ºF (180ºC).
Butter or spray a round 8-inch cake pan (22cm).
Working a hand mixer (or stand mixer) in a large bowl, beat 2 eggs adding ¼ cup white sugar and ½ cup packed brown sugar gradually and beating for another 2 minutes, until thick and lighter in color.
Add ½ cup sunflower oil in a thin stream, beating for a minute or two, until it thickens.
Add 1 teaspoon orange zest and 1 ½ teaspoons pure vanilla extract and mix well.
Reduce the mixer speed to low speed and add the sifted dry ingredients (flour, salt, and baking powder) in 2 parts, mixing only until they are incorporated. You can sift them directly over the oil batter or sift them in a different bowl and then add.
Run a spatula around the bowl and under the batter, just to make sure there are no dry spots, then scrape the batter into the pan and smooth the top.
Arrange 7 or 8 red plums cut in wedges in a circle, or however you want. Sprinkle 1 tablespoon brown sugar on top.
Bake for about 45 minutes, or until top is brown and puffed around the plums that are juicy and wrinkled, and a tester inserted into the center comes out clean. Ovens are all different so it might take a little more or a little less time to fully bake.
Transfer to a wire rack and cool, then run a knife around the sides of the pan and remove the cake.
Serve at room temperature, plain with a sprinkle of powdered sugar.