Cut the sweet potato, onion, and apple into 1/2-inch cubes or pieces and set each aside separately. Slice the pork into 12 to 14 medallions about 3/4- to 1-inch thick (don’t worry if they’re not all even). Season them with 1 tsp. salt and a little pepper and set aside.
Melt 1 Tbs. each of the butter and oil in a large straightsided skillet over medium heat. Add the sweet potato pieces in one layer and season with about 3/4 tsp. salt and a little pepper. Sauté them until they’re brown and crusty on most sides, about 10 minutes. (Don’t stir often; let them sit in the pan for 2 or 3 minutes on each side before flipping with a metal spatula.) Carefully add 3 Tbs. water to the pan, and, as it sizzles, cover the pan briefly (about 1 minute) to let the potato steam. Uncover, stir, and transfer to a bowl.
Turn the heat to medium high, heat another 1 Tbs. each butter and oil in the pan, and add the onion and apple. Season with 1/2 tsp. salt. Sauté, stirring occasionally, until the onion is soft and both the onion and apple are nicely browned around the edges (the bottom of the pan will be brown), 6 to 8 minutes. Stir in the ginger, sauté briefly, and pour 2 Tbs. cider vinegar and 2 Tbs. water into the pan. Remove the pan from the heat and stir to scrape up the browned bits. Transfer the contents of the pan to the bowl with the sweet potatoes.
Put the pan back over medium-high heat and add the remaining 1 Tbs. butter and 1 Tbs. oil. As soon as the butter sizzles loudly, add the pork medallions in one layer. Cook for 2 minutes (they’ll be lightly browned), turn over, and cook for another 2 minutes. Transfer the pork to a plate. Carefully pour in the remaining 2 Tbs. cider vinegar and 2 Tbs. water, remove the pan briefly from the heat, and scrape up the browned bits. Return the sweet potato mixture to the pan over the heat and stir until heated through. Put several pork slices in the middle of each of two or three warm plates. Fold the parsley, if using, into the sweet potato mixture and evenly mound it on top of the pork.