Flatten each pork slice to 3/4 inch by placing it between sheets of plastic wrap and pounding it with a meat mallet or rolling pin. Sprinkle both sides of pork with thyme and salt. Warm oil over medium-high heat in a large heavy skillet. Cook medallions, turning once, until well browned on both sides, about 3 minutes total. (Work in batches, if necessary.) Transfer to a plate.
Add butter to pan and melt. Add onion and cook until softened, about 3 minutes. Add broth, jam and mustard and bring to a boil, stirring. Cover, lower heat and simmer until onion is very soft, about 5 minutes.
Return pork to pan, turning to coat with sauce. Cover and simmer until pork is cooked through, about 5 minutes. Transfer pork to a platter, cover with sauce and serve immediately.