Sprinkle the meat with salt and pepper and lightly dredge in flour. Heat the oil in a Dutch oven over medium-high heat. Brown the meat in batches and remove to a plate, adding a little additional oil when necessary. When all of the meat is browned and set aside, add the butter to the Dutch oven to melt. When the butter foams, add the celery, carrots, onions, bay leaf, herb bundle, some salt and pepper and the caraway seeds. Stir to combine and sweat the vegetables for a few minutes. Add the cider and vinegar, and reduce by half. Add the stock and then return the pork to the Dutch oven. Cover and cook about 1 hour over low heat or in an oven preheated to 325 degrees F.
Stir in the potatoes and apples and continue to cook until the pork is tender, 30 to 40 minutes.
Cool and store for a make-ahead meal. Reheat over moderate heat and garnish with celery tops to serve.
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