Remove the pork from the refrigerator 30–40 minutes before cooking. Pat completely dry with paper towels, then season all sides generously with salt and black pepper, pressing the seasoning into the meat.
Preheat your oven to 325°F (165°C).
Heat olive oil in a Dutch oven over medium-high heat until shimmering, then sear the pork roast on all sides — including the ends — for about 4–5 minutes per side until deep golden-brown (15–20 minutes total). Transfer the seared pork to a plate and set aside.
Reduce heat to medium and cook the quartered onions in the pot for 5–6 minutes, then add smashed garlic and cook 1 minute more. Stir in the Dijon mustard, cinnamon, and nutmeg to coat the aromatics.
Pour in the apple cider, scraping up all browned bits from the bottom of the pot. Add chicken broth and maple syrup, stir to combine, and bring to a gentle simmer.
Nestle the carrots, celery, and apple wedges into the pot, then add the thyme, rosemary, and bay leaves. Return the seared pork to the pot so it sits about halfway submerged in liquid.
Cover the Dutch oven and transfer to the preheated oven. Cook for 3 to 3.5 hours, turning the roast every hour, until the internal temperature reaches 195–205°F (90–96°C) and the meat pulls apart easily with a fork.
Transfer the pork and vegetables to a serving platter and tent loosely with foil. Let rest for 15–20 minutes while you prepare the sauce.
Strain the cooking liquid through a fine-mesh sieve into a bowl, then skim excess fat from the surface with a spoon.
Return the strained liquid to the pot over medium heat and bring to a simmer. Whisk together cornstarch and cold water, then stir into the liquid and cook 2–3 minutes until thickened to your desired consistency. Season with salt and pepper.
Slice or pull apart the pork into generous portions, arrange with the roasted vegetables on a platter, drizzle with sauce, and serve the remaining gravy on the side.