For the beef:
Heat the oven to 325°F and arrange a rack in the lower third.
Pat the roast dry with paper towels and trim any excess fat or sinew. Season generously with salt and pepper; set aside.
Heat the oil in a large, heavy-bottomed pot or Dutch oven over medium-high heat until shimmering. Add the roast and cook, turning occasionally, until it’s browned all over, about 15 to 20 minutes total. Transfer to a large plate and set aside. Meanwhile, peel and cut the carrots into large dice; set aside. Cut the celery and onions into large dice.
Add the carrots, celery, and onions to the pot and season with salt and pepper. Cook, stirring occasionally, until the vegetables have softened and are just starting to brown, about 5 to 7 minutes.
Add the wine, scrape up any browned bits from the bottom of the pot, and bring to a boil. Cook, stirring occasionally, until the wine is reduced by half, about 7 minutes. Meanwhile, peel any loose outer skins from the garlic head and cut off the top quarter to expose the cloves (reserve the top for another use).
Add the broth or stock, vinegar, garlic head, thyme, bay leaves, and rosemary, stir to combine, and bring to a boil. Return the roast and any accumulated juices on the plate to the pot.
Cover with a tightfitting lid and place in the oven. Cook, flipping the roast every hour, until the beef is fork tender, about 3 hours total. Meanwhile, make the gremolata.
For the gremolata:
Peel, core, and cut the apples into small dice. Place the apples in a medium nonreactive bowl, add the parsley, olive oil, and zest, season with salt and pepper, and toss to combine. Taste and season with additional salt and pepper as needed, cover, and refrigerate.
To serve:
Remove and discard the herbs and garlic from the pot. Break the beef into large chunks, top with the gremolata, and serve with the sauce.
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