Preheat the oven to 400 degrees F (200 degrees C).

Heat oil in a large, oven-proof skillet over medium-high heat. Generously season pork tenderloin with salt and black pepper. Cook tenderloin in hot oil until browned on all sides, 2 to 4 minutes per side. Transfer tenderloin to a plate and set aside.

Sauté onion and a pinch of salt in drippings in the skillet until onion begins to soften, 3 to 5 minutes. Add shallots; reduce heat to medium. Cook and stir until onion and shallots are golden brown and caramelized, about 10 minutes.

Stir thyme into onion mixture, then place tenderloin on top. Set plums, skin-side down, around tenderloin. Transfer the skillet to the 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 clean plate; cover with aluminum foil to keep warm.

Place the skillet over medium-high heat. Pour water and vinegar into onion mixture. Bring 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 in cold butter until melted and sauce is shiny.

Pour sauce over sliced pork and plums to serve.