Preheat oven to 400 degrees F (200 degrees C). Generously season pork tenderloin with salt and black pepper.

Heat oil in a large, oven-proof skillet over medium-high heat. Cook tenderloin until browned on all sides, 2 to 4 minutes per side. Transfer tenderloin to a plate.

Saute onion with a pinch of salt in the same skillet until just softening, 3 to 5 minutes. Add shallots, reduce heat to medium, and cook and stir until shallots and onion are golden brown and caramelized, about 10 minutes.

Stir thyme into onion mixture; place tenderloin over onion mixture, and set plum quarters, skin-side down, around pork tenderloin. Transfer skillet to preheated oven.

Cook until pork is slightly pink in the center, about 20 minutes. An instant-read thermometer inserted into the center should read at least 145 degrees F (63 degrees C). Transfer pork and plums to a plate.

Place skillet over medium-high heat and pour water and balsamic vinegar into onion mixture. Bring mixture to a boil while scraping the browned bits of food off of the bottom of the pan with a wooden spoon. Cook and stir until liquid is reduced by half, 5 to 10 minutes; remove from heat. Whisk butter into mixture until melted and sauce is shiny. Pour sauce over pork and plums.