Preheat oven to 350°F. Pat the pork dry with paper towels. Season on all sides with salt and pepper.
Heat butter and olive oil in a large Dutch oven over medium-high heat until it is hot but not smoking. Sear the pork on all sides (about 4-6 minutes per side), just until a nice golden-brown color develops and the meat releases easily from the pan. You don’t need to cook the pork all of the way through since it will finish in the oven. Remove to a plate.
Reduce the heat to medium and add 1 cup of the chicken broth, scraping with a wooden spoon to deglaze the pan (loosening all of the browned bits from the bottom). Add the potatoes, carrots, onion, celery, and garlic to the pot. Cook, stirring, until the onions are translucent (about 10 minutes). Season with salt and pepper to taste.
Place the pork on top of the vegetables. Add the remaining 1 cup of chicken broth, apple cider, thyme, rosemary, and bay leaf. Cover and bake in the 350°F oven until the pork reaches an internal temperature of 145°F, about 20-25 minutes. Remove the pork to a plate; tent with foil.
Increase the oven temperature to 400°F, return the pot to the oven, and continue roasting the vegetables for about 15 more minutes, or until they’re fork-tender. Slice the pork and serve with the vegetables.