Heat a large heavy bottomed skillet over medium-high heat. Dry the pork medallions well and season with salt and pepper. Add the oil to the skillet and heat until shimmering. Lay the pork in the pan and cook until browned on the first side, about 4 minutes. Turn and cook until the second side is browned, about 3 minutes more. Transfer the pork to a plate, and cover loosely with foil.
Add the onions to the skillet, stir and season with salt and pepper. Cover, and reduce heat to medium and cook until soft, about 8 minutes. Add the cider vinegar and stir, scraping up the browned bits that cling to the skillet. Add the onions to the pork.
Add butter to skillet, raise heat to medium-high. Add the apples and sage; cook, stirring occasionally, until golden, about 3 minutes. Stir in the broth and mustard, and simmer until the apples soften, about 2 minutes. Return the onions and any accumulated juices from the pork to the skillet. Simmer to thicken slightly, about 2 minutes. Nestle the pork in the onions and heat until the meat is warmed through.
Divide the pork medallions among 4 plates and smother them with apples and onions. Serve.
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