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Heat oil in a 6- to 8-quart Dutch oven until almost smoking. Brown pork on all sides in the hot oil. Transfer browned pork to a plate and discard fat.
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Add apple cider, onion, salt, and pork to the Dutch oven. Bring to a boil then reduce heat to simmer. Cover and simmer until meat is tender, about 2 to 2 1/2 hours.
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Remove pork and place on a cutting board. Let rest for 10 to 15 minutes. Slice and place on a serving platter. Cover with foil to keep warm.
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Core apples and cut into wedges. Cut dried apricots in half (if not already in pieces).
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Add apples, apricots, cardamom, and cinnamon to the dutch oven. Bring to a boil then reduce heat to simmer. Cover and simmer until fruit in tender, about 5 minutes.
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Use a slotted spoon to transfer apples and apricots to the serving platter. Re-cover with foil to keep warm until serving.
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Bring the juices in the Dutch oven to a gentle boil and cook until reduced to 1 cup, about 7 to 10 minutes.
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Spoon cider sauce over meat and fruit or serve on the side.