Heat oven to 425°F. Trim silver skin from pork without removing large pieces of meat. Pat dry and season with salt and pepper. Heat oil in a 12-inch ovenproof skillet over medium-high heat. Sear pork on all sides, turning with tongs, 6–8 minutes total. Transfer to a clean plate; it is not cooked through yet.

Reduce heat to medium. Add apples and onion to the same skillet and cook 5 minutes, turning gently, until starting to soften and brown. If the pan is very dry, add 1 tablespoon of the measured broth rather than extra oil.

Brush seared pork with mustard and sprinkle with thyme, reserving a pinch of fresh leaves for serving if desired. Set it on the apples and onions. Roast 12–20 minutes, checking early, until an instant-read thermometer in the thickest part reads at least 145°F. If apples are already tender, lift them out while pork finishes.

Transfer pork to a clean cutting board and rest loosely covered for 5 minutes, never less than 3 minutes. Protect your hand from the hot skillet handle. Place skillet over medium heat, add remaining broth and vinegar, and scrape up browned bits. Simmer 3–5 minutes to reduce slightly and finish softening the apples and onions if needed. Stir in butter.

Slice rested pork crosswise into 3/4-inch medallions. Divide among four plates with apples, onions, and sauce. Add the reserved pinch of fresh thyme, if using.

Refrigerate leftovers in shallow containers within 2 hours, or 1 hour above 90°F. Use within 3–4 days. Reheat covered with a splash of broth until pork reaches 165°F.