Heat the oil in a large, deep skillet over medium-high heat. Sprinkle salt and pepper all over the pork chops and add to the pan. Cook, turning once, until browned, about 4 minutes. Transfer to a plate.
Add the onion, mushrooms, and a pinch each of salt and pepper to the pan. Cook, stirring occasionally, until tender, about 6 minutes. Add the flour and cook, stirring, for 2 minutes. Continue stirring while adding the broth in a slow, steady stream. Bring to a boil, then simmer, scraping the browned bits from the pan until the consistency of gravy, about 5 minutes. Stir in the Worcestershire sauce.
Return the pork chops to the pan and simmer until the pork is not longer pink in the center, about 5 minutes. Transfer the pork to serving dishes. Stir the spinach into the sauce until just wilted, about 1 minute. Nestle the pork into the sauce and serve.