Heat the oven to 220 C / 425 F with a rack in the middle. Pat the tenderloins dry, trim off any silver skin, and rub them with 3/4 tsp salt, the pepper and the thyme.
Heat 1 1/2 tsp of the oil in a 30 cm / 12-inch oven-safe cast-iron skillet over medium-high heat for 2 minutes, until it shimmers. Sear one tenderloin for 5 to 6 minutes, turning every 1 to 2 minutes, until browned on all sides. Move it to a plate, add another 1 1/2 tsp oil, and sear the second tenderloin the same way.
Reduce the heat to medium. Add the remaining 1 tbsp oil and the onion, and cook for 4 minutes, scraping up the browned bits, until softened. Add the apple wedges and garlic and cook for 2 minutes, until the garlic is fragrant.
Stir in the broth, mustard, vinegar and 1/4 tsp salt, then add the beans. Simmer for 3 minutes, then turn off the heat.
Tuck the thin tail of each tenderloin under itself and nestle both on top of the beans, pouring in any juices from the plate. Roast uncovered for 12 to 15 minutes, checking from 12 minutes, until a thermometer in the thickest part reads 145 F / 63 C. The center will be faintly blush pink.
Wearing a mitt, set the hot skillet on the stovetop. Move the pork to a cutting board and rest it for 5 minutes, then slice it into 1.5 cm rounds. Stir the beans, spoon them onto plates, top with the pork, and sprinkle with parsley.