Get ready. Preheat oven to 350F, spray a 10" tart pan with cake spray, and measure or weigh out your ingredients: flours, baking poweder, and salt in one bowl, sugar in another bowl, butter alone, olive oil alone. Have the extracts on hand but don't necessarily measure those out yet. Pit/Slice your plums.
Make the cake batter. First thing is the butter. Throw into the stand mixer on a medium speed and whip until it's soft, probably a minute or so. Then olive oil -- toss it in and mix on the same speed for another minute. Then pour in the sugar. 1 minute on medium. Then the eggs, add one then mix for a few seconds; add the other egg, then mix for a few seconds. Then the extract. I looove almond extract so this is where i deviated from the NYT recipe -- i did equal amounts of vanilla and almond extract. LAST, add in the flours by thirds and mix on the LOWEST speed until it's JUST incorporated. The more you mix, the more the glutenz activate in the flour and the tougher the batter becomes.
Prepare for oven and bake. For me this was a thick batter so had to spread it around. I, fairly carelessly, arranged the plums on top. Bake for 40 minutes. You'll know it's done with the top is light brown and the cake has just pulled away from the sides of the pan.
Finish and enjoy. Remove from oven and let cool completely; serve with some whipped cream or ice cream if you wish!