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1
Place rack in lower third of oven; preheat to 325u00b0. Heat oil medium heat. Add bacon, stirring often, until browned and crisp, 6-8 minutes. Using a slotted spoon, transfer bacon to a paper towel-lined plate.
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2
Increase heat to medium-high. Add butter to pot with drippings. Season pork shoulder with salt and pepper. Cook pork shoulder until brown on all sides, 8-10 minutes per batch. Transfer pork shoulder to a plate.
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3
Add shallots to pot and cook, stirring often, until shallots begin to soften, about 4 minutes. Remove pot from heat; add Calvados and stir, scraping up browned bits from bottom of pot. Return to heat and simmer for 1 minute. Add apple cider and vinegar. Bring to a simmer, then return pork shoulder to pot, placing in a single layer on bottom of pot (the meat should not be completely covered). Last time I made this, I doubled the braising liquid, and there was still not enough sauce. Try triple next time? Cover pot and transfer to oven. Braise pork shoulder, turning after 1 hour, until fork-tender, about 2 hours. Using tongs, transfer pork to a deep platter. Add reserved bacon. Skim fat from cooking liquid. Place pot over medium heat and bring liquid to a simmer. Add apples and cook until apples are just tender and sauce is slightly reduced, 8-10 minutes.
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4
Stir Dijon mustard into sauce; season with salt, pepper, and more vinegar, if desired. Pour sauce with apples over pork on platter. Sprinkle with chives.